(one of the interesting forwards that I got)

If you know a distinctive fact about a number not listed here, I think you are the next math genius. I was shocked, baffeled, head over heels and what not after seeing this information.

primes graphs digits sums of powers bases

combinatorics powers/polygonal Fibonacci

geometry repdigits algebra perfect/amicable

pandigital matrices divisors games/puzzles

0 is the additive identity.

1 is the multiplicative identity.

2 is the only even prime.

3 is the number of spatial dimensions we live in.

4 is the smallest number of colors sufficient to color all planar maps.

5 is the number of Platonic solids.

6 is the smallest perfect number.

7 is the smallest number of faces of a regular polygon that is not constructible by straightedge and compass.

8 is the largest cube in the Fibonacci sequence.

9 is the maximum number of cubes that are needed to sum to any positive integer.

10 is the base of our number system.

11 is the largest known multiplicative persistence.

12 is the smallest abundant number.

13 is the number of Archimedian solids.

14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.

15 is the smallest composite number n with the property that there is only one group of order n.

16 is the only number of the form xy = yx with x and y different integers.

17 is the number of wallpaper groups.

18 is the only number (other than 0) that is twice the sum of its digits.

19 is the maximum number of 4th powers needed to sum to any number.

20 is the number of rooted trees with 6 vertices.

21 is the smallest number of distinct squares needed to tile a square.

22 is the number of partitions of 8.

23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.

24 is the largest number divisible by all numbers less than its square root.

25 is the smallest square that can be written as a sum of 2 squares.

26 is the only positive number to be directly between a square and a cube.

27 is the largest number that is the sum of the digits of its cube.

28 is the 2nd perfect number.

29 is the 7th Lucas number.

30 is the largest number with the property that all smaller numbers relatively prime to it are prime.

31 is a Mersenne prime.

32 is the smallest non-trivial 5th power.

33 is the largest number that is not a sum of distinct triangular numbers.

34 is the smallest number with the property that it and its neighbors have the same number of divisors.

35 is the number of hexominoes.

36 is the smallest non-trivial number which is both square and triangular.

37 is the maximum number of 5th powers needed to sum to any number.

38 is the last Roman numeral when written lexicographically.

39 is the smallest number which has 3 different partitions into 3 parts with the same product.

40 is the only number whose letters are in alphabetical order.

41 is a value of n so that x2 + x + n takes on prime values for x = 0, 1, 2, ... n-2.

42 is the 5th Catalan number.

43 is the number of sided 7-iamonds.

44 is the number of derangements of 5 items.

45 is a Kaprekar number.

46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.

47 is the largest number of cubes that cannot tile a cube.

48 is the smallest number with 10 divisors.

49 is the smallest number with the property that it and its neighbors are squareful.

50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.

51 is the 6th Motzkin number.

52 is the 5th Bell number.

53 is the only two digit number that is reversed in hexadecimal.

54 is the smallest number that can be written as the sum of 3 squares in 3 ways.

55 is the largest triangular number in the Fibonacci sequence.

56 is the number of reduced 5×5 Latin squares.

57 = 111 in base 7.

58 is the number of commutative semigroups of order 4.

59 is the number of stellations of an icosahedron.

60 is the smallest number divisible by 1 through 6.

61 is the 3rd secant number.

62 is the smallest number that can be written as the sum of of 3 distinct squares in 2 ways.

63 is the number of partially ordered sets of 5 elements.

64 is the smallest number with 7 divisors.

65 is the smallest number that becomes square if its reverse is either added to or subtracted from it.

66 is the number of 8-iamonds.

67 is the smallest number which is palindromic in bases 5 and 6.

68 is the 2-digit string that appears latest in the decimal expansion of π.

69 has the property that n2 and n3 together contain each digit once.

70 is the smallest weird number.

71 divides the sum of the primes less than it.

72 is the maximum number of spheres that can touch another sphere in a lattice packing in 6 dimensions.

73 is the smallest multi-digit number which is one less than twice its reverse.

74 is the number of different non-Hamiltonian polyhedra with a minimum number of vertices.

75 is the number of orderings of 4 objects with ties allowed.

76 is an automorphic number.

77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.

78 is the smallest number that can be written as the sum of of 4 distinct squares in 3 ways.

79 is a permutable prime.

80 is the smallest number n where n and n+1 are both products of 4 or more primes.

81 is the square of the sum of its digits.

82 is the number of 6-hexes.

83 is the number of strongly connected digraphs with 4 vertices.

84 is the largest order of a permutation of 14 elements.

85 is the largest n for which 12+22+32+ ... +n2 = 1+2+3+ ... +m has a solution.

86 = 222 in base 6.

87 is the sum of the squares of the first 4 primes.

88 is the only number known whose square has no isolated digits.

89 = 81 + 92

90 is the number of degrees in a right angle.

91 is the smallest pseudoprime in base 3.

92 is the number of different arrangements of 8 non-attacking queens on an 8×8 chessboard.

93 = 333 in base 5.

94 is a Smith number.

95 is the number of planar partitions of 10.

96 is the smallest number that can be written as the difference of 2 squares in 4 ways.

97 is the smallest number with the property that its first 3 multiples contain the digit 9.

98 is the smallest number with the property that its first 5 multiples contain the digit 9.

99 is a Kaprekar number.

100 is the smallest square which is also the sum of 4 consecutive cubes.

101 is the number of partitions of 13.

102 is the smallest number with three different digits.

103 has the property that placing the last digit first gives 1 more than triple it.

104 is the smallest known number of unit line segments that can exist in the plane, 4 touching at every vertex.

105 is the largest number n known with the property that n - 2k is prime for k>1.

106 is the number of trees with 10 vertices.

107 is the exponent of a Mersenne prime.

108 is 3 hyperfactorial.

109 has a 5th root that starts 2.555555....

110 is the smallest number that is the product of two different substrings.

111 is the smallest possible magic constant of a 3×3 magic square of distinct primes.

112 is the side of the smallest square that can be tiled with distinct integer-sided squares.

113 is a permutable prime.

114 = 222 in base 7.

115 is the number of rooted trees with 8 vertices.

116 is a value of n for which n! + 1 is prime.

117 is the smallest possible value of the longest edge in a Heronian Tetrahedron.

118 is the smallest number that has 4 different partitions into 3 parts with the same product.

119 is the smallest number n where either n or n+1 is divisible by the numbers from 1 to 8.

120 is the smallest number to appear 6 times in Pascal's triangle.

121 is the only square known of the form 1 + p + p2 + p3 + p4, where p is prime.

122 is the smallest number n>1 so that n concatenated with n-1 0's concatenated with the reverse of n is prime.

123 is the 10th Lucas number.

124 is the smallest number with the property that its first 3 multiples contain the digit 2.

125 is the only number known that contains all its proper divisors as proper substrings.

126 = 9C4.

127 is a Mersenne prime.

128 is the largest number which is not the sum of distinct squares.

129 is the smallest number that can be written as the sum of 3 squares in 4 ways.

130 is the number of functions from 6 unlabeled points to themselves.

131 is a permutable prime.

132 is the smallest number which is the sum of all of the 2-digit numbers that can be formed with its digits.

133 is the smallest number n for which the sum of the proper divisors of n divides φ(n).

134 = 8C1 + 8C3 + 8C4.

135 = 11 + 32 + 53.

136 is the sum of the cubes of the digits of the sum of the cubes of its digits.

137 is the smallest prime with 3 distinct digits that remains prime if one of its digits is removed.

138 is a value of n for which n!!! - 1 is prime.

139 is the number of unlabeled topologies with 5 elements.

140 is the smallest harmonic divisor number.

141 is the 6th central trinomial coefficient.

142 is the number of planar graphs with 6 vertices.

143 is the smallest quasi-Carmichael number in base 8.

144 is the largest square in the Fibonacci sequence.

145 is a factorion.

146 = 222 in base 8.

147 is the number of sided 6-hexes.

148 is the number of perfect graphs with 6 vertices.

149 is the smallest number whose square begins with three 2's.

150 = 100101102 = 21124 = 11005, each using 2 different digits an equal number of times.

151 is a palindromic prime.

152 has a square composed of the digits 0-4.

153 is a narcissistic number.

154 is the smallest number which is palindromic in bases 6, 8, and 9.

155 is the sum of the primes between its smallest and largest prime factor.

156 is the number of graphs with 6 vertices.

157 is the largest number known whose square contains the same digits as the square of its successor.

158 is the number of planar partitions of 11.

159 is the number of isomers of C11H24.

160 is the number of 9-iamonds.

161 is a Cullen number.

162 is the smallest number that can be written as the sum of of 4 positive squares in 9 ways.

163 is the largest Heegner Number.

164 is the smallest number which is the concatenation of squares in two different ways.

165 is the midpoint of the nth larger prime and nth smaller prime, for 1 ≤ n ≤ 6.

166 is the number of monotone Boolean functions of 4 variables.

167 is the smallest number whose 4th power begins with 4 identical digits

168 is the size of the smallest non-cyclic simple group which is not an alternating group.

169 is the 7th Pell number.

170 is the smallest number n for which φ(n) and σ(n) are both square.

171 has the same number of digits in Roman numerals as its cube.

172 = 444 in base 6.

173 has a square containing only 2 digits.

174 is the smallest number that can be written as the sum of of 4 positive distinct squares in 6 ways.

175 = 11 + 72 + 53.

176 is an octagonal pentagonal number.

177 is the number of graphs with 7 edges.

178 has a cube with the same digits as another cube.

179 has a square comprised of the digits 0-4.

180 is the total number of degrees in a triangle.

181 is a strobogrammatic prime.

182 is the number of connected bipartite graphs with 8 vertices.

183 is the smallest number n so that n concatenated with n+1 is square.

184 is a Kaprekar constant in base 3.

185 is the number of conjugacy classes in the automorphism group of the 8 dimensional hypercube.

186 is the number of degree 11 irreducible polynomials over GF(2).

187 is the smallest quasi-Carmichael number in base 7.

188 is the number of semigroups of order 4.

189 is a Kaprekar constant in base 2.

190 is the largest number with the property that it and its ditinct prime factors are palindromic in Roman numerals.

191 is a number n for which n, n+2, n+6, and n+8 are all prime.

192 is the smallest number with 14 divisors.

193 is the largest number that can be written as ab + ac + bc with 0 < 198 =" 11" 205 =" 5" 41 =" 5416." 215 =" 555" 243 =" 35." 246 =" 9C2">1 for which the arithmetic, geometric, and harmonic means of φ(n) and σ(n) are all integers.

249 is the index of a prime Woodall number.

250 is the smallest multi-digit number so that the sum of the squares of its prime factors equals the sum of the squares of its digits.

251 is the smallest number that can be written as the sum of 3 cubes in 2 ways.

252 is the 5th central binomial coefficient.

253 is the smallest non-trivial triangular star number.

254 is the smallest composite number all of whose proper divisors contain the digit 2.

255 = 11111111 in base 2.

256 is the smallest non-trivial 8th power.

257 is a Fermat prime.

258 is a value of n so that n(n+9) is a palindrome.

259 = 1111 in base 6.

260 is the number of ways that 6 non-attacking bishops can be placed on a 4×4 chessboard.

261 is the number of essentially different ways to dissect a 16-gon into 7 quadrilaterals.

262 is the 5th meandric number and the 9th open meandric number.

263 is the largest known prime whose square is strobogrammatic.

264 is the largest known number whose square is undulating.

265 is the number of derangements of 6 items.

266 is the Stirling number of the second kind S(8,6).

267 is the number of planar partitions of 12.

268 is the smallest number whose product of digits is 6 times the sum of its digits.

269 is the number of 6-octs.

270 is a harmonic divisor number.

271 is the smallest prime p so that p-1 and p+1 are divisible by cubes.

272 is the 4th tangent number.

273 = 333 in base 9.

274 is the Stirling number of the first kind s(6,2).

275 is the number of partitions of 28 in which no part occurs only once.

276 = 15 + 25 + 35.

277 is a Perrin number.

278 is the closest integer to 6π.

279 is the maximum number of 8th powers needed to sum to any number.

280 is the number of ways 18 people around a round table can shake hands in a non-crossing way, up to rotation.

281 is the sum of the first 14 primes.

282 is the number of planar partitions of 9.

283 = 25 + 8 + 35.

284 is an amicable number.

285 is the number of binary rooted trees with 13 vertices.

286 is the number of rooted trees with 9 vertices.

287 is the sum of consecutive primes in 3 different ways.

288 is the smallest non-palindrome non-square that when multiplied by its reverse is a square.

289 is a Friedman number.

290 has a base 3 representation that ends with its base 6 representation.

291 is the largest number that is not the sum of distinct non-trivial powers.

292 is the number of ways to make change for a dollar.

293 is the number of ways to stack 20 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

294 is the number of planar 2-connected graphs with 7 vertices.

295 is a structured deltoidal hexacontahedral number.

296 is the number of partitions of 30 into distinct parts.

297 is a Kaprekar number.

298 is a value of n so that n(n+3) is a palindrome.

299 is the maximum number of regions a cube can be cut into with 12 cuts.

300 is the largest possible score in bowling.

301 is a 6-hyperperfect number.

302 is the number of ways to play the first 3 moves in Checkers.

303 is the number of bipartite graphs with 8 vertices.

304 is a primitive semiperfect number.

305 is an hexagonal prism number.

306 is the number of 5-digit triangular numbers.

307 is a non-palindrome with a palindromic square.

308 is a heptagonal pyramidal number.

309 is the smallest number whose 5th power contains every digit at least once.

310 = 1234 in base 6.

311 is a permutable prime.

312 = 2222 in base 5.

313 is the number of intersections when all the diagonals of a regular dodecagon are drawn.

314 is the smallest number that can be written as the sum of of 3 positive distinct squares in 6 ways.

315 = (4+3) × (4+1) × (4+5).

316 has a digit product which is the digit sum of (31)6.

317 is a value of n for which one less than the product of the first n primes is prime.

318 is the number of unlabeled partially ordered sets of 6 elements.

319 is the smallest number with the property that the partition with the largest product does not have a maximum number of parts.

320 is the maximum determinant of a binary 10×10 matrix.

321 is a Delannoy number.

322 is the 12th Lucas number.

323 is the product of twin primes.

324 is the largest possible product of positive integers with sum 16.

325 is a 3-hyperperfect number.

326 is the number of permutations of some subset of 5 elements.

327 is the largest number n so that n, 2n, and 3n together contain every digit from 1-9 exactly once.

328 concatenated with its successor is square.

329 is the number of forests with 10 vertices.

330 = 11C4.

331 is both a centered pentagonal number and a centered hexagonal number.

332 is the number of 2-connected graphs with 7 vertices

333 is the number of 7-hexes.

334 is the number of trees on 13 vertices with diameter 7.

335 is the number of degree 12 irreducible polynomials over GF(2).

336 = 8P3.

337 is the number of different resistances that can be created in a circuit of 8 equal resistors.

338 is the smallest number for which both the number of divisors and the sum of its prime factors is a perfect number.

339 is the number of ways to divide 5 black and 5 white beads into piles.

340 is a value of n for which n! + 1 is prime.

341 is the smallest pseudoprime in base 2.

342 is the number of inequivalent binary linear codes of length 8.

343 is a strong Friedman number.

344 is the smallest number that can be written as the sum of a cube and a 7th power in more than one way.

345 is half again as large as the sum of its proper divisors.

346 is a Franel number.

347 is a Friedman number.

348 is the smallest number whose 5th power contains exactly the same digits as another 5th power.

349 is a tetranacci number.

350 is the Stirling number of the second kind S(7,4).

351 is the smallest number so that it and the surrounding numbers are all products of 4 or more primes.

352 is the number of different arrangements of 9 non-attacking queens on an 9×9 chessboard.

353 is the smallest number whose 4th power can be written as the sum of four 4th powers.

354 is the sum of the first four 4th powers.

355 is the number of labeled topologies with 4 elements.

356 ???

357 has a base 3 representation that ends with its base 7 representation.

358 has a base 3 representation that ends with its base 7 representation.

359 has a base 3 representation that ends with its base 7 representation.

360 is the number of degrees in a circle.

361 is the number of intersections on a Go board.

362 and its double and triple all use the same number of digits in Roman numerals.

363 is a perfect totient number.

364 = 14C3.

365 is the smallest number that can be written as a sum of consecutive squares in more than 1 way.

366 is the number of days in a leap year.

367 is the largest number whose square has strictly increasing digits.

368 is the number of ways to tile a 4×15 rectangle with the pentominoes.

369 is the number of octominoes.

370 is a narcissistic number.

371 is a narcissistic number.

372 is a hexagonal pyramidal number.

373 is a permutable prime.

374 is the smallest number that can be written as the sum of 3 squares in 8 ways.

375 is a truncated tetrahedral number.

376 is an automorphic number.

377 is the 14th Fibonacci number.

378 is the maximum number of regions a cube can be cut into with 13 cuts.

379 is a value of n for which one more than the product of the first n primes is prime.

380 is the number of necklaces possible with 13 beads, each being one of 2 colors.

381 is a Kaprekar constant in base 2.

382 is the smallest number n with σ(n) = σ(n+3).

383 is the number of Hamiltonian graphs with 7 vertices.

384 = 8!! = 12!!!!.

385 is the number of partitions of 18.

386 is the number of regions the complex plane is cut into by drawing lines between all pairs of 11th roots of unity.

387 ???

388 is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 6 stamps.

389 is the smallest prime so that it and the next 3 primes are all equal to 1 (mod 4).

390 is the number of partitions of 32 into distinct parts.

391 ???

392 is a Kaprekar constant in base 5.

393 is the 7th central trinomial coefficient.

394 is a Schröder number.

395 does not occur in its factorial in base 2.

396 is the number of 3×3 sliding puzzle positions that require exactly 11 moves to solve starting with the hole in a corner.

397 is a Cuban prime.

398 is the number of integers with complexity 22.

399 is a Lucas-Carmichael number.

400 = 1111 in base 7.

401 is the number of connected planar Eulerian graphs with 9 vertices.

402 is the number of graphs with 8 vertices and 9 edges.

403 is the product of two primes which are reverses of each other.

404 is the number of sided 10-hexes with holes.

405 is a pentagonal pyramidal number.

406 is the number of ways to tile a 3×17 rectangle with 3×1 rectangles.

407 is a narcissistic number.

408 is the 8th Pell number.

409 is the number of graphs with 8 vertices with clique number 2.

410 is the smallest number that can be written as the sum of 2 distinct prime powers in 2 ways.

411 is a member of the Fibonacci-type sequence starting with 1 and 4.

412 is the number of subsets of {1,2,3,...,11} that have a sum divisible by 5.

413 is a structured hexagonal diamond number.

414 is a value of n for which n4, n5, n6, and n7 have the same digit sum.

415 ???

416 is the number of subsets of the 15th roots of unity that add to a real number.

417 is the smallest number so that it and the next 3 numbers have different numbers of distinct prime factors.

418 has the property that the sum of its prime factors is equal to the product of its digits.

419 is the number of ways to divide a 6×6 grid of points into two sets using a straight line.

420 is the smallest number divisible by 1 through 7.

421 is the number of commutative monoids of order 6.

422 is the smallest number whose 8th power has 21 digits.

423 is a number that does not have any digits in common with its cube.

424 ???

425 is the number of subsets of {1,2,3,...,11} that have an integer average.

426 is a stella octangula number.

427 is a value of n for which n! + 1 is prime.

428 has the property that its square is the concatenation of two consecutive numbers.

429 is the 7th Catalan number.

430 is the number of necklaces possible with 6 beads, each being one of 4 colors.

431 is the index of a prime Fibonacci number.

432 = 4 × 33 × 22.

433 is the index of a prime Fibonacci number.

434 is the smallest composite value of n for which σ(n) + 2 = σ(n+2).

435 is the number of ordered partitions of 16 into distinct parts.

436 is the smallest number whose cube contains four 8's.

437 has a cube with the last 3 digits the same as the 3 digits before that.

438 = 666 in base 8.

439 is the smallest prime where inserting the same digit between every pair of digits never yields another prime.

440 is the number of permutations of 12 items that fix 9 elements.

441 is the smallest square which is the sum of 6 consecutive cubes.

442 is the number of planar partitions of 13.

443 is a value of n for which σ(n) is a repdigit.

444 is the largest known n for which there is a unique integer solution to a1+ ... +an = (a1)...(an).

445 has a base 10 representation which is the reverse of its base 9 representation.

446 is the smallest number that can be written as the sum of 3 distinct squares in 8 ways.

447 is the smallest number of convex quadrilaterals formed by 15 points in general position.

448 is the number of 10-iamonds.

449 has a base 3 representation that begins with its base 7 representation.

450 is the number of 13-iamonds with holes.

451 is the smallest number whose reciprocal has period 10.

452 is the closest integer to 7π.

453 is the only number n so that n, 2n, and 6n together contain every digit exactly once.

454 is the largest number known that cannot be written as a sum of 7 or fewer cubes.

455 = 15C3.

456 is the number of tournaments with 7 vertices.

457 is the index of a prime Euclid number.

458 is a number that does not have any digits in common with its cube.

459 is the smallest number n for which reverse(n) - n contains the same digits as n.

460 ???

461 is the number of ways to stack 18 pennies in contiguous rows so that each penny lies on the table or on two pennies.

462 = 11C5.

463 is the smallest prime so that it and the next 6 primes are all equal to 3 (mod 4).

464 is the maximum number of regions space can be divided into by 12 spheres.

465 is a Kaprekar constant in base 2.

466 = 1234 in base 7.

467 has strictly increasing digits in bases 7, 9, and 10.

468 = 3333 in base 5.

469 is a value of n for which n! - 1 is prime.

470 has a base 3 representation that ends with its base 6 representation.

471 is the smallest number with the property that its first 4 multiples contain the digit 4.

472 is the number of ways to tile a 5×5 square with integer-sided squares.

473 is the largest known number whose square and 4th power use different digits.

474 is a member of the Fibonacci-type sequence starting with 1 and 8.

475 has a square that is composed of overlapping squares of smaller numbers.

476 is the number of different products of subsets of the set {1, 2, 3, ... 11}.

477 is the smallest number whose cube contains four 3's.

478 is the 7th Pell-Lucas number.

479 is the number of sets of distinct positive integers with mean 6.

480 is the smallest number which can be written as the difference of 2 squares in 8 ways.

481 is the number of conjugacy classes in the automorphism group of the 10 dimensional hypercube.

482 is a number whose square and cube use different digits.

483 is the last 3-digit string in the decimal expansion of π.

484 is a palindrome in base 3 and in base 10.

485 is the number of categories with 6 morphisms and 2 objects.

486 is a Perrin number.

487 is the number of Hadamard matrices of order 28.

489 is an octahedral number.

490 is the number of partitions of 19.

491 is the smallest number n so that the largest prime factors of the numbers n through n+4 decrease.

492 is a hexanacci number.

493 is a Lucas 7-step number.

494 is the number of unlabeled distributive lattices with 14 elements.

495 is the Kaprekar constant for 3-digit numbers.

496 is the 3rd perfect number.

497 is the number of graphs with 8 edges.

498 is the number of necklaces possible with 8 beads, each being one of 3 colors.

499 is the number of ways to place 26 points on a 13×13 grid so that no 3 points are on a line.

500 is the number of planar partitions of 10.

501 is the number of partitions of 5 items into ordered lists.

502 uses the same digits as φ(502).

503 is the smallest prime which is the sum of the cubes of the first few primes.

504 = 9P3.

505 = 10C5 + 10C0 + 10C5.

506 is the sum of the first 11 squares.

507 is the number of rooted ternary trees with 10 vertices.

508 ???

509 is the index of a prime Fibonacci number.

510 is the number of binary rooted trees with 14 vertices.

511 = 111111111 in base 2.

512 is the cube of the sum of its digits.

513 is the number of conjugacy classes of the alternating group A22.

514 ???

515 is the number of graphs on 6 vertices with no isolated vertices.

516 is the number of partitions of 32 in which no part occurs only once.

517 does not occur in its factorial in base 2.

518 = 51 + 12 + 83.

519 is the number of trees on 15 vertices with diameter 5.

520 is the number of ways to place 2 non-attacking kings on a 6×6 chessboard.

521 is the 13th Lucas number.

522 is the number of ways to place a non-attacking white and black pawn on a 6×6 chessboard.

523 is the smallest prime that is followed by 17 composite numbers.

524 is the number of 6-kings.

525 is a hexagonal pyramidal number.

526 is the number of ways to cut a 8×8 chessboard into 2 pieces with equal areas with a cut that only travels up and right.

527 is the smallest number n for which there do not exist 4 smaller numbers so that a1! a2! a3! a4! n! is square.

528 concatenated with its successor is square.

529 is the smallest number n so that the continued fraction for n/k contains no 2's for any 1 ≤ k ≤ n.

530 is the sum of the first 3 perfect numbers.

531 is the smallest number with the property that its first 4 multiples contain the digit 1.

532 is a hendecagonal pyramidal number.

533 is the number of degree sequences for graphs with 5 vertices.

534 ???

535 is a palindrome whose φ(n) is also palindromic.

536 is the number of solutions of the stomachion puzzle.

537 divides the sum of the cubes of the first 537 primes.

538 is the 10th open meandric number.

539 is the number of multigraphs with 5 vertices and 9 edges.

540 is divisible by its reverse.

541 is the number of orderings of 5 objects with ties allowed.

542 is a member of the Fibonacci-type sequence starting with 3 and 8.

543 is a number whose square and cube use different digits.

544 is the generalized Catalan number C(14,3).

545 has a base 3 representation that begins with its base 4 representation.

546 undulates in bases 3, 4, and 5.

547 is the smallest number that can not be written using 11 copies of 11 and the operations +, –, ×, and ÷.

548 is the maximum number of 9th powers needed to sum to any number.

549 ???

550 is a pentagonal pyramidal number.

551 is the number of trees with 12 vertices.

552 is the number of prime knots with 11 crossings.

553 is a Huay rhombic dodecahedral number.

554 is the number of self-dual planar graphs with 20 edges.

555 is a repdigit.

556 are the first 3 digits of 4556.

557 ???

558 divides the sum of the largest prime factors of the first 558 positive integers.

559 is a centered cube number.

560 = 16C3.

561 is the smallest Carmichael number.

562 is the maximum number of regions a circle can be cut into by joining 11 points on the circumference with straight lines.

563 is the largest known Wilson prime.

564 is the number of 13-ominoes with a horizontal or vertical line of symmetry.

565 is a structured truncated octahedral number.

566 is the number of ways to place 24 points on a 12×12 grid so that no 3 points are on a line.

567 has the property that it and its square together use the digits 1-9 once.

568 is the smallest number whose 7th power can be written as the sum of seven 7th powers.

569 is the smallest number n for which the concatenation of n, (n+1), ... (n+30) is prime.

570 is the product of all the prime palindromic Roman numerals.

571 is the index of a prime Fibonacci number.

572 is the smallest number which has equal numbers of every digit in bases 2 and 3.

573 has the property that its square is the concatenation of two consecutive numbers.

574 is the maximum number of pieces a torus can be cut into with 14 cuts.

575 is a palindrome that is one less than a square.

576 is the number of 4×4 Latin squares.

577 is a Proth prime.

578 is the number of graphs with 7 vertices with clique number 3.

579 is the number of graphs with 7 vertices that have chromatic number 3.

580 is the 6th central quadrinomial coefficient.

581 has a base 3 representation that begins with its base 4 representation.

582 is the number of antisymmetric relations on a 5 element set.

583 is the smallest number whose reciprocal has period 26.

584 is the number of ways to color the vertices of a triangle with 12 colors, up to rotation.

585 is a palindrome in base 2, base 8, and in base 10.

586 is the smallest number that appears in its factorial 6 times.

587 is the smallest number whose digit sum is larger than that of its cube.

588 is the number of possible rook moves on a 7×7 chessboard.

589 is a centered tetrahedral number.

590 is a value of n for which φ(n) + φ(n+1) divides σ(n) + σ(n+1).

591 is the number of ways to stack 23 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

592 evenly divides the sum of its rotations.

593 is a Leyland number.

594 = 15 + 29 + 34.

595 is the number of ways to tile a 3×18 rectangle with 3×1 rectangles.

596 is the number of Hamiltonian cycles of a 4×9 rectangle graph.

597 is a value of n for which n!!! + 1 is prime.

598 = 51 + 92 + 83.

599 is the smallest number whose digits add to 23.

600 and its reverse are both the averages of twin primes.

601 is the location of the first occurrence of 3 consecutive zeroes in the decimal digits of π.

602 are the first 3 digits of 5602.

603 is the smallest number n so that n, n+1, and n+2 are all the product of a prime and the square of a prime.

604 and the two numbers before it and after it are all products of exactly 3 primes.

605 has a sum of digits equal to its largest prime factor.

606 is the first non-trivial number that is both 11-gonal and centered 11-gonal.

607 is the exponent of a Mersenne prime.

608 is a number that does not have any digits in common with its cube.

609 is a strobogrammatic number.

610 is the smallest Fibonacci number that begins with 6.

611 ???

612 is a number whose square and cube use different digits.

613 is the index of a prime Lucas number.

614 is the smallest number that can be written as the sum of 3 squares in 9 ways.

615 is the trinomial coefficient T(10,6).

616 is a Padovan number.

617 = 1!2 + 2!2 + 3!2 + 4!2.

618 is the number of ternary square-free words of length 15.

619 is a strobogrammatic prime.

620 is the number of sided 7-hexes.

621 is the number of ways to 9-color the faces of a tetrahedron.

622 ???

623 is the number of inequivalent asymmetric Ferrers graphs with 23 points.

624 is the smallest number with the property that its first 5 multiples contain the digit 2.

625 is an automorphic number.

626 is a palindrome in base 5 and in base 10.

627 is the number of partitions of 20.

628 is the sum of the squares of 4 consecutive primes.

629 evenly divides the sum of its rotations.

630 is a triangular number, 3 times a triangular number, and 6 times a triangular number.

631 has a base 2 representation that begins with its base 5 representation.

632 is the number of necklaces (that can't be turned over) possible with 13 beads, each being one of 2 colors.

633 is the smallest number n whose 5th root has a decimal part that begins with the digits of n.

634 is a number n whose 5th root has a decimal part that begins with the digits of n.

635 is a number n whose 5th root has a decimal part that begins with the digits of n.

636 is a number n whose 5th root has a decimal part that begins with the digits of n.

637 = 777 in base 9.

638 is the number of fixed 5-kings.

639 is a number n whose 5th root has a decimal part that begins with the digits of n.

640 = 16!!!!!!.

641 is the smallest prime factor of 225+1.

642 is the smallest number with the property that its first 6 multiples contain the digit 2.

643 is the largest prime factor of 123456.

644 is a Perrin number.

645 is the largest n for which 1+2+3+ ... +n = 12+22+32+ ... +k2 for some k.

646 is the number of connected planar graphs with 7 vertices.

647 ???

648 is the smallest number whose decimal part of its 6th root begins with the digits 1-9 in some order.

650 is the sum of the first 12 squares.

651 has a 4th power that is the sum of four 4th powers.

652 is the only known non-perfect number whose number of divisors and sum of smaller divisors are perfect.

653 is the only known prime for which 5 is neither a primitive root or a quadratic residue of 4n2+1.

654 has a square that is the sum of a cube and 5th power.

655 ???

656 is a palindrome in base 3 and in base 10.

657 is the number of ways to tile a 4×22 rectangle with 4×1 rectangles.

658 is the number of triangles of any size contained in the triangle of side 13 on a triangular grid.

659 is an Eisenstein-Mersenne prime.

660 is the order of a non-cyclic simple group.

661 is the largest prime factor of 8! + 1.

662 is the index of the smallest triangular number that contains the digits 1, 2, 3, 4, and 5.

663 is the generalized Catalan number C(15,3).

664 is a value of n so that n(n+7) is a palindrome.

665 is a member of the Fibonacci-type sequence starting with 1 and 4.

666 is the largest rep-digit triangular number.

667 is the number of asymmetric trees with 16 vertices.

668 is the number of legal pawn moves in Chess.

669 is the number of unsymmetrical ways to dissect a regular 12-gon into 10 triangles.

670 is an octahedral number.

671 is a rhombic dodecahedral number.

672 is a multi-perfect number.

673 is a tetranacci number.

674 ???

675 is the smallest order for which there are 17 groups.

676 is the smallest palindromic square number whose square root is not palindromic.

677 is the closest integer to 11e.

678 is a member of the Fibonacci-type sequence starting with 1 and 7.

679 is the smallest number with multiplicative persistence 5.

680 is the smallest tetrahedral number that is also the sum of 2 tetrahedral numbers.

681 divides the sum of the first 681 composite numbers.

682 = 11C6 + 11C8 + 11C2.

683 is a Wagstaff prime.

684 is the sum of 3 consecutive cubes.

685 ???

686 is the number of partitions of 35 in which no part occurs only once.

687 is the closest integer to 8π.

688 is a Friedman number.

689 is the smallest number that can be written as the sum of 3 distinct squares in 9 ways.

690 is the smallest number that can not be written as the sum of a triangular number, a cube, and a Fibonacci number.

691 is the smallest prime p for which x5 = x4 + x3 + x2 + x + 1 (mod p) has 5 solutions.

692 is a number that does not have any digits in common with its cube.

693 are the first 3 decimal digits of ln(2).

694 is the number of different arrangements (up to rotation and reflection) of 7 non-attacking rooks on a 7×7 chessboard.

695 is the maximum number of pieces a torus can be cut into with 15 cuts.

696 is a palindrome n so that n(n+8) is also palindromic.

697 is a 12-hyperperfect number.

698 ???

699 is a value of n for which cos(n) is smaller than any previous integer.

700 is the number of symmetric 8-cubes.

701 = 10 + 21 + 32 + 43 + 54.

702 ???

703 is a Kaprekar number.

704 is the number of sided octominoes.

705 is the smallest Lucas pseudoprime.

706 ???

707 is the smallest number whose reciprocal has period 12.

708 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps.

709 is the number of connected planar graphs with 9 edges.

710 is the number of connected graphs with 9 edges.

711 ???

712 is the largest number known that does not have any digits in common with its 8th power.

713 is the number of commutative monoids of order 7 with 4 idempotents.

714 is the smallest number which has equal numbers of every digit in bases 2 and 5.

715 = 13C4.

716 is the smallest number whose cube contains four 6's.

717 is a palindrome in base 2 and in base 10.

718 is the number of unlabeled topologies with 6 elements.

719 is the number of rooted trees with 10 vertices.

720 = 6!

721 is the smallest number which can be written as the difference of 2 cubes in 2 ways.

722 is the sum of the 4th powers of the first 3 primes.

723 ???

724 is the number of different arrangements of 10 non-attacking queens on an 10×10 chessboard.

725 ???

726 is a pentagonal pyramidal number.

727 has the property that its square is the concatenation of two consecutive numbers.

728 is the smallest number n where n and n+1 are both products of 5 or more primes.

729 = 36.

730 is the number of connected bipartite graphs with 9 vertices.

731 is the number of planar partitions of 14.

732 = 17 + 26 + 35 + 44 + 53 + 62 + 71.

733 is the sum of the digits of 444.

734 is the smallest number that can be written as the sum of 3 distinct non-zero squares in 10 ways.

735 is the smallest number that is the concatenation of its distinct prime factors.

736 is a strong Friedman number.

737 ???

738 = 6 + 66 + 666.

739 has a base 2 representation that begins with its base 9 representation.

740 is the number of self-avoiding walks of length 8.

741 is the number of multigraphs with 6 vertices and 8 edges.

742 is the smallest number that is one more than triple its reverse.

743 is the number of independent sets of the graph of the 4-dimensional hypercube.

744 is the number of perfect squared rectangles of order 14.

745 is the smallest number whose square begins with three 5's.

746 = 17 + 24 + 36.

747 ???

748 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner.

749 is the number of ways to divide a 7×7 grid of points into two sets using a straight line.

750 is the Stirling number of the second kind S(10,8).

751 is the index of a prime Woodall number.

752 is the number of conjugacy classes in the automorphism group of the 11 dimensional hypercube.

753 is the smallest number whose cube contains 4 consecutive 7's.

754 ???

755 is the number of trees on 14 vertices with diameter 6.

756 is the maximum number of regions space can be divided into by 14 spheres.

757 is the smallest number whose reciprocal has a period of 27.

758 ???

759 ???

760 is the number of partitions of 37 into distinct parts.

761 ???

762 is the starting location of 999999 in the decimal expansion of π.

763 is the smallest number whose 4th power contains every digit at least once.

764 is the number of 8×8 symmetric permutation matrices.

765 is a Kaprekar constant in base 2.

766 is the number of series-reduced planted trees with 9 leaves.

767 is the largest n so that n2 = mC0 + mC1 + mC2 + mC3 has a solution.

768 is the number of subsets of {1,2,3,...,12} that have an integer average.

769 is the total number of digits of all binary numbers of length 1-7.

770 is the number of digits of the 15th perfect number.

771 is the number of intersections when all the diagonals of a regular 14-gon are drawn.

772 ???

773 is the smallest odd number n so that n+2k is composite for all k 7.

3110 = 22222 in base 6.

3114 has a square containing only 2 digits.

3115 has the property that if each digit is replaced by its square, the resulting number is a cube.

3119 is a right-truncatable prime.

3120 is the product of the first 6 Fibonacci numbers.

3121 = 31215 + 31217 + 31218.

3122 is the number of ordered sequences of coins totaling 29 cents.

3124 = 44444 in base 5.

3125 is a strong Friedman number.

3126 is a Sierpinski Number of the First Kind.

3127 is the product of two consecutive primes.

3135 is the smallest order of a cyclotomic polynomial whose factorization contains 7 as a coefficient.

3136 is a square that remains square if all its digits are decremented.

3137 is the number of planar partitions of 17.

3139 is the 9th central trinomial coefficient.

3141 is the integer part of 1000 π.

3146 is a structured deltoidal hexacontahedral number.

3148 has a square with the first 3 digits the same as the next 3 digits.

3150 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

3156 is the sum of its proper divisors that contain the digit 5.

3159 is the number of trees with 14 vertices.

3160 is the largest known value of n for which 2nCn is not divisible by the first 5 primes.

3161 is the smallest number whose square begins with three 9's.

3163 is the smallest number whose square has 7 digits.

3168 has a square whose reverse is also a square.

3169 is a Cuban prime.

3171 is the sum of the squares of 3 consecutive primes.

3174 is the first of four consecutive squareful numbers.

3178 = 4321 in base 9.

3179 is the number of 13-ominoes that tile the plane by translation.

3180 has a base 3 representation that ends with its base 5 representation.

3181 has a base 3 representation that ends with its base 5 representation.

3182 has a base 3 representation that ends with its base 5 representation.

3184 is a value of n for which cos(n) is smaller than any previous integer.

3185 is the number of ways to legally add 2 sets of parentheses to a product of 13 variables.

3186 is a value of n for which 2nCn is not divisible by 3, 5, or 7.

3187 is the smallest value of n for which n and 8n together use each digit 1-9 exactly once.

3190 is a narcissistic number in base 7.

3191 is the smallest number whose reciprocal has period 29.

3192 is the number of planar graphs with 8 vertices, all with degree 2 or more.

3200 is the number of graceful permutations of length 13.

3203 has the property that if each digit is replaced by its square, the resulting number is a square.

3210 is the smallest 4-digit number with decreasing digits.

3212 = 37 + 29 + 17 + 29.

3214 is the maximum number of regions a circle can be cut into by joining 17 points on the circumference with straight lines.

3216 is the smallest number with the property that its first 6 multiples contain the digit 6.

3217 is the exponent of a Mersenne prime.

3218 has the property that the concatenation of its prime factors in increasing order is a square.

3225 is the number of symmetric 3×3 matrices in base 5 with determinant 0.

3226 is the number of 12-iamonds without holes.

3229 is a value of n for which one more than the product of the first n primes is prime.

3232 is the number of isomers of C12H24 without any double bonds.

3240 is the number of 3×3×3 Rubik's cube positions that require exactly 3 moves to solve.

3242 has a square with the first 3 digits the same as the next 3 digits.

3244 is the number of asymmetric trees with 18 vertices.

3248 is the number of legal bishop moves in Chess.

3249 is the smallest square that is comprised of two squares that overlap in one digit.

3250 is a value of n for which 2nCn is not divisible by 3, 5, or 7.

3251 is a number n for which n, n+2, n+6, and n+8 are all prime.

3252 is the number of graphs with 9 vertices and 11 edges.

3254 = 33 + 2222 + 555 + 444.

3259 = 33 + 2222 + 5 + 999.

3262 is the number of graphs with 9 vertices that have 6 automorphisms.

3264 is the number of partitions of 49 into distinct parts.

3267 = 12345 in base 7.

3274 = 3030224 = 1010445, each using 3 different digits exactly twice.

3276 = 28C3.

3277 is an Euler pseudoprime.

3280 = 11111111 in base 3.

3281 is the sum of consecutive squares in 2 ways.

3282 is the sum of its proper divisors that contain the digit 4.

3283 is the number of 3×3 sliding puzzle positions that require exactly 15 moves to solve starting with the hole on a side.

3290 is an enneagonal pyramidal number.

3292 is the number of ways to tile a 4×27 rectangle with 4×1 rectangles.

3294 is a value of n for which 6n and 7n together use each digit exactly once.

3297 is a value of n for which 5n and 7n together use each digit exactly once.

3300 is the number of non-isomorphic groupoids on 4 elements.

3301 is a value of n for which the nth Fibonacci number begins with the digits in n.

3302 is the maximum number of pieces a torus can be cut into with 26 cuts.

3303 is a centered octahedral number.

3304 is the maximum number of regions a cube can be cut into with 27 cuts.

3305 is the number of rectangles with corners on an 10×10 grid of points.

3311 is the sum of the first 21 squares.

3312 = 332 + 122.

3313 is the smallest prime number where every digit d occurs d times.

3318 has exactly the same digits in 3 different bases.

3320 has a base 4 representation that ends with 3320.

3321 has a base 4 representation that ends with 3321.

3322 has a base 4 representation that ends with 3322.

3323 has a base 4 representation that ends with 3323.

3324 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 20 stamps.

3325 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with integer dimensions less than 13.

3326 is the smallest integer ratio of a 17-digit number to its product of digits.

3329 is a Padovan number.

3330 is a value of n for which n-1 and n+1 are twin primes, and so are 2n-1 and 2n+1.

3331 is the number of monoids of order 7 with 3 idempotents.

3333 is a repdigit.

3334 is the number of 12-iamonds.

3335 is the smallest number whose square contains 4 consecutive 2's.

3337 has a cube with only odd digits.

3338 is a member of the Fibonacci-type sequence starting with 3 and 7.

3340 = 3333 + 3 + 4 + 0.

3341 = 3333 + 3 + 4 + 1.

3342 = 3333 + 3 + 4 + 2.

3343 = 3333 + 3 + 4 + 3.

3344 = 3333 + 3 + 4 + 4.

3345 = 3333 + 3 + 4 + 5.

3346 = 3333 + 3 + 4 + 6.

3347 = 3333 + 3 + 4 + 7.

3348 = 3333 + 3 + 4 + 8.

3349 = 3333 + 3 + 4 + 9.

3358 is the sum of the squares. of the first 11 primes.

3360 = 16P3.

3361 is the number of quasi-triominoes that fit inside a 12×12 grid.

3366 = (19 + 29 + 39) / (1 × 2 × 3).

3367 is the smallest number which can be written as the difference of 2 cubes in 3 ways.

3368 is the number of ways that 8 non-attacking bishops can be placed on a 5×5 chessboard.

3369 is a Kaprekar constant in base 4.

3375 is a Friedman number.

3376 is the number of digits of the 23rd Mersenne prime.

3378 is a Friedman number.

3379 is a number whose square and cube use different digits.

3380 would be prime if preceded and followed by a 1, 3, 7, or 9.

3381 is the number of ways to 14-color the faces of a tetrahedron.

3382 is a value of n for which 2φ(n) = φ(n+1).

3383 has the property that the sum of its prime factors is equal to the product of its digits.

3390 is a value of n for which n-1 and n+1 are twin primes, and so are 2n-1 and 2n+1.

3400 is a truncated tetrahedral number.

3402 can be written as the sum of 2, 3, 4, or 5 positive cubes.

3403 is a triangular number that is the product of two primes.

3404 is the number of binary partitions of 38.

3405 is a structured great rhombicosidodecahedral number.

3411 is the number of inequivalent asymmetric Ferrers graphs with 31 points.

3413 = 11 + 22 + 33 + 44 + 55.

3417 is a hexagonal pyramidal number.

3420 is the order of a non-cyclic simple group.

3427 is a member of the Fibonacci-type sequence starting with 1 and 5.

3431 is the number of inequivalent Ferrers graphs with 31 points.

3432 is the 7th central binomial coefficient.

3433 is a narcissistic number in base 6.

3435 = 33 + 44 + 33 + 55.

3439 is a rhombic dodecahedral number.

3440 is the closest integer to 20e.

3444 is a stella octangula number.

3447 is the smallest value of n for which 2n and 5n together use the digits 1-9 exactly once.

3451 is the number of conjugacy classes of the alternating group A31.

3456 has digits in arithmetic sequence.

3457 is a Proth prime.

3459 has a 6th root that starts 3.88888....

3461 is a number n for which n, n+2, n+6, and n+8 are all prime.

3465 = 15!!!!.

3468 = 682 - 342.

3472 is the number of ways to place 2 non-attacking bishops on a 8×8 chessboard.

3476 is a value of n for which n!! - 1 is prime.

3478 has the property that dropping its first and last digits gives its largest prime factor.

3480 is a Perrin number.

3486 has a square that is formed by 3 squares that overlap by 1 digit.

3487 is the number of squares in a 14×14 grid of squares with diagonals drawn.

3488 has a 5th root that starts 5.11111....

3489 is the smallest number whose square has the first 3 digits the same as the last 3 digits.

3492 is the number of labeled semigroups of order 4.

3498 is a number whose sum of divisors is a 5th power.

3501 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

3507 is a value of n for which n! - 1 is prime.

3510 = 6666 in base 8.

3511 is the largest known Wieferich prime.

3521 = 3333 + 55 + 22 + 111.

3522 is the sum of its proper divisors that contain the digit 7.

3525 is a Pentanacci number.

3527 is the number of ways to fold a strip of 10 stamps.

3528 is an Achilles number.

3531 is a value of n for which φ(n) = φ(n-2) - φ(n-1).

3536 is a heptagonal pyramidal number.

3539 is a value of n for which cos(n) is smaller than any previous integer.

3541 is the smallest number whose reciprocal has period 20.

3542 is the number of ways to write 16 as an ordered sum of positive integers, where adjacent numbers are different.

3543 has a cube containing only 3 different digits.

3552 is a value of n for which n φ(n) is a palindrome.

3563 is a house number.

3564 divides 11 + 22 + 33 + . . . + 35643564.

3570 is both a triangular number and 6 times a triangular number.

3571 is the 17th Lucas number.

3577 is a Kaprekar constant in base 2.

3579 has digits in arithmetic sequence.

3583 is the smallest number requiring an addition chain of length 16.

3584 is not the sum of 4 non-zero squares.

3585 has a 10th power that contains the same digits as 90369.

3588 is the maximum number of regions space can be divided into by 23 spheres.

3593 is a prime that is the average of two 4th powers.

3594 is the smallest number whose 9th power has 32 digits.

3596 is the number permutations of {1,2,3,...,19} where adjacent numbers differ by no more than 2.

3599 is the product of twin primes.

3600 is the order of a perfect group.

3605 is a centered tetrahedral number.

3607 is a prime factor of 123456789.

3609 is the number of multigraphs with 22 vertices and 4 edges.

3610 is a value of n for which n! - 1 is prime.

3612 is a narcissistic number in base 7.

3613 is a narcissistic number in base 7.

3616 = 1111 in base 15.

3620 is the trinomial coefficient T(16,12).

3624 is the first of five consecutive squareful numbers.

3626 is a member of the Fibonacci-type sequence starting with 1 and 9.

3630 appears inside its 4th power.

3632 is a value of n for which n φ(n) is a palindrome.

3635 has a square with the first 3 digits the same as the next 3 digits.

3638 is the number of ways to stack 26 pennies in contiguous rows so that each penny lies on the table or on two pennies.

3640 = 13!!!.

3641 is an hexagonal prism number.

3645 is the maximum determinant of a binary 12×12 matrix.

3648 is the number of subsets of {1,2,3,...,15} that have a sum divisible by 9.

3650 is the number of binary cube-free words of length 19.

3654 = 29C3.

3655 is the sum of consecutive squares in 2 ways.

3657 is a structured truncated octahedral number.

3658 is the number of forests with 13 vertices.

3663 is a palindrome in base 8 and in base 10.

3664 is the number of graphs with 10 vertices and 9 edges.

3665 would be prime if preceded and followed by a 1, 3, 7, or 9.

3671 is the number of 9-abolos.

3673 is the number of ways a 8×1 rectangle can be surrounded by 8×1 rectangles.

3678 has a square comprised of the digits 1-8.

3679 is the number of ways to stack 17 pennies in a line so that each penny lies on the table or on two pennies.

3681 is the maximum number of pieces a torus can be cut into with 27 cuts.

3683 is the maximum number of regions a cube can be cut into with 28 cuts.

3684 is a Keith number.

3685 is a strong Friedman number.

3686 would be prime if preceded and followed by a 1, 3, 7, or 9.

3696 is the number of ways to color the vertices of a square with 11 colors, up to rotation.

3697 is the smallest number in base 6 whose square contains the same digits in the same proportion.

3698 has a square comprised of the digits 0-7.

3700 is the sum of the squares of 4 consecutive primes.

3702 = 3 + 33 + 333 + 3333.

3703 is the smallest number that can not be formed using the digit 1 at most 26 times, together with the symbols +, –, × and ÷.

3705 is the generalized Catalan number C(16,4).

3709 is a value of n for which 2n and 7n together use the digits 1-9 exactly once.

3710 is a number whose sum of divisors is a 5th power.

3711 is the number of multigraphs with 6 vertices and 10 edges.

3715 is a member of the Fibonacci-type sequence starting with 3 and 8.

3718 is the number of partitions of 28.

3720 = 225 + 226 + . . . + 240 = 241 + 242 + . . . + 255.

3721 is the number of partitions of 46 in which no part occurs only once.

3723 has a 4th power that is the sum of four 4th powers.

3728 is the smallest number whose 7th power has 25 digits.

3729 is a value of n for which n and 5n together use each digit 1-9 exactly once.

3731 is a dodecagonal pyramidal number.

3733 is a right-truncatable prime.

3734 is the number of binary partitions of 39.

3739 is a right-truncatable prime.

3740 is the sum of consecutive squares in 2 ways.

3743 is the number of polyaboloes with 9 half squares.

3745 has a square with the last 3 digits the same as the 3 digits before that.

3747 is the smallest number whose 9th power contains exactly the same digits as another 9th power.

3750 is the first of four consecutive squareful numbers.

3751 has the same digits as the 3751st prime.

3752 is a cubic star number.

3753 has a cube that is the sum of 3 positive cubes.

3760 is a substring of any power of itself.

3761 is the first year of the modern Hebrew calendar.

3763 is the largest n so that Q(√n) has class number 6.

3765 is the number of series-reduced planted trees with 18 vertices.

3767 is the smallest number with complexity 28.

3771 is a value of n for which 4n and 7n together use each digit exactly once.

3773 is a structured great rhombicubeoctahedral number.

3780 is a highly abundant number.

3784 has a factorization using the same digits as itself.

3786 = 34 + 74 + 8 + 64.

3789 divides the sum of the digits of 3789!.

3791 is the number of symmetric plane partitions of 30.

3792 occurs in the middle of its square.

3793 is a right-truncatable prime.

3795 is the sum of the first 22 squares.

3797 is a right-truncatable prime.

3798 is a value of n for which 2n and 9n together use the digits 1-9 exactly once.

3803 is the largest prime factor of 123456789.

3804 is a member of the Fibonacci-type sequence starting with 2 and 5.

3807 and its successor are both divisible by 4th powers.

3808 is the generalized Catalan number C(12,5).

3810 is the number of ways to place a non-attacking white and black pawn on a 9×9 chessboard.

3812 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 21 stamps.

3813 is the number of partitions of 47 in which no part occurs only once.

3816 is a truncated cube number.

3822 is the number of triangles of any size contained in the triangle of side 24 on a triangular grid.

3824 is the number of lines through exactly 2 points of a 12×12 grid of points.

3825 is a Kaprekar constant in base 2.

3832 is the number of fixed 6-kings.

3836 is the maximum number of inversions in a permutation of length 7.

3840 = 10!!

3843 is a value of n for which 7n and 9n together use each digit exactly once.

3846 is the number of Hamiltonian cycles of a 4×11 rectangle graph.

3849 has a square with the first 3 digits the same as the next 3 digits.

3850 is a structured octagonal anti-diamond number.

3859 is a member of the Fibonacci-type sequence starting with 2 and 9.

3861 is the smallest number whose 4th power starts with 5 identical digits.

3864 is a strong Friedman number.

3871 is the sum of the cubes of 3 consecutive primes.

3872 is an Achilles number.

3873 is a Kaprekar constant in base 4.

3876 = 19C4.

3882 is the sum of its proper divisors that contain the digit 4.

3883 is the smallest number whose cube contains 4 consecutive 6's.

3884 has a 5th root that starts 5.22222....

3888 is an Achilles number.

3889 + φ(3889) = 7777.

3894 is an octahedral number.

3895 is the number of intersections when all the diagonals of a regular 19-gon are drawn.

3897 divides the sum of the digits of 3897!.

3900 has a base 2 representation that is two copies of its base 5 representation concatenated.

3901 has a base 2 representation that ends with its base 5 representation.

3903 is a Lucas 7-step number.

3906 = 111111 in base 5.

3907 = 15628 / 4, and each digit is contained in the equation exactly once.

3910 is the number of 3×3 sliding puzzle positions that require exactly 28 moves to solve starting with the hole in a corner.

3911 and its reverse are prime, even if we append or prepend a 3 or 9.

3912 is a value of n for which 5n and 7n together use each digit exactly once.

3913 is a Huay rhombic dodecahedral number.

3916 is a triangular number whose internal digits are triangular and whose external digits are triangular.

3920 = (5+3) × (5+9) × (5+2) × (5+0).

3925 is a centered cube number.

3926 is the 12th open meandric number.

3927 has an 8th root whose decimal part starts with the digits 1-9 in some order.

3928 is the closest integer to 21e.

3929 is the number of integers with complexity 29.

3937 is a Kaprekar constant in base 2.

3938 is the number of 4×4 sliding puzzle positions that require exactly 11 moves to solve starting with the hole in a corner.

3939 is a structured truncated tetrahedral number.

3942 is a value of n for which n and 4n together use each digit 1-9 exactly once.

3952 has a sum of digits equal to its largest prime factor.

3956 is the number of conjugacy classes in the automorphism group of the 15 dimensional hypercube.

3957 is the number of ways to stack 32 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

3960 is a highly abundant number.

3967 is the smallest number whose 12th power contains exactly the same digits as another 12th power.

3968 and its successor are both divisible by 4th powers.

3969 is a Kaprekar constant in base 2.

3972 is a strong Friedman number.

3973 has a 4th power that is the sum of four 4th powers.

3977 has the property that dropping its first and last digits gives its largest prime factor.

3978 is the number of ways to place 30 points on a 15×15 grid so that no 3 points are on a line.

3982 is the smallest number whose 5th power has 18 digits.

3983 has the property that the concatenation of its prime factors in increasing order is a square.

3984 is a heptanacci number.

3985 = 3333 + 9 + 88 + 555.

3986 has an 8th root that starts 2.81881881....

3987 is the closest integer to 14π.

3996 = (66 + 67 + 68 + 69) / (6 × 7 × 8 × 9).

3999 is the smallest number whose digits add to 30.

4000 has a cube that contains only even digits.

4002 has a square with the first 3 digits the same as the next 3 digits.

4004 = (10 × 11 × 12 × 13 × 14) / (10 + 11 + 12 + 13 + 14) .

4005 is a triangular number whose internal digits are triangular and whose external digits are triangular.

4006 = 14C4 + 14C0 + 14C0 + 14C6.

4008 has a square with the last 3 digits the same as the 3 digits before that.

4010 is the magic constant of a 20×20 magic square.

4011 is the sum of the squares of 3 consecutive primes.

4013 is a prime factor of 1111111111111111111111111111111111.

4019 is a prime that remains prime if any digit is deleted.

4023 is the number of ways to tile a 3×23 rectangle with 3×1 rectangles.

4029 is the number of regions formed when all diagonals are drawn in a regular 19-gon.

4030 is a weird number.

4031 is the sum of the cubes of the first 6 primes.

4032 is the number of connected bipartite graphs with 10 vertices.

4033 is an Euler pseudoprime.

4037 is a member of the Fibonacci-type sequence starting with 1 and 6.

4040 is an enneagonal pyramidal number.

4047 is a hexagonal pyramidal number.

4048 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

4050 has the property that dropping its first and last digits gives its largest prime factor.

4051 is the number of partitions of 6 items into ordered lists.

4053 has a cube that contains only digits 5 and larger.

4055 is the smallest number whose cube contains six 6's.

4056 is the number of possible rook moves on a 13×13 chessboard.

4059 is the sum of 3 consecutive cubes.

4060 = 30C3.

4062 is the smallest number with the property that its first 8 multiples contain the digit 2.

4064 is a value of n for which σ(n) = σ(reverse(n)).

4071 is the number of ways to color the vertices of a triangle with 23 colors, up to rotation.

4074 is a value of n for which σ(n) = 2reverse(n).

4080 = 17P3.

4083 is the number of ways 12 people can line up so that only one person has a taller person in front of him.

4087 is the product of two consecutive primes.

4088 is the maximum number of pieces a torus can be cut into with 28 cuts.

4089 is a centered octahedral number.

4090 is the maximum number of regions a cube can be cut into with 29 cuts.

4093 = 28651 / 7, and each digit is contained in the equation exactly once.

4094 is the Entringer number E(8,2).

4095 and its reverse are both differences of positive 4th powers.

4096 is the smallest number with 13 divisors.

4097 is the smallest number (besides 2) that can be written as the sum of two cubes or the sum of two 4th powers.

4098 is the number of subsets of the 26th roots of unity that add to 1.

4099 has a square with the last 3 digits the same as the 3 digits before that.

4100 = 5555 in base 9.

4104 can be written as the sum of 2 cubes in 2 ways.

4106 is a Friedman number.

4112 is the number of necklaces possible with 17 beads, each being one of 2 colors.

4116 is the number of necklaces (that can't be turned over) possible with 16 beads, each being one of 2 colors.

4120 has a cube with a digit sum larger than its 7th power.

4121 is a number whose product of digits is equal to its sum of digits.

4124 is the number of binary partitions of 40.

4128 is the smallest number with the property that its first 10 multiples contain the digit 2.

4140 is the 8th Bell number.

4141 = 41415 + 41417 + 41418.

4147 is a value of n for which φ(n) = φ(reverse(n)).

4149 is a value of n for which σ(n-1) = σ(n+1).

4150 = 45 + 15 + 55 + 05.

4151 = 45 + 15 + 55 + 15.

4152 = 45 + 15 + 55 + 2.

4153 = 45 + 15 + 55 + 3.

4154 = 45 + 15 + 55 + 4.

4155 = 45 + 15 + 55 + 5.

4156 = 45 + 15 + 55 + 6.

4157 = 45 + 15 + 55 + 7.

4158 = 45 + 15 + 55 + 8.

4159 = 45 + 15 + 55 + 9.

4160 = 43 + 163 + 03.

4161 = 43 + 163 + 13.

4163 is the number of inequivalent asymmetric Ferrers graphs with 32 points.

4167 is a Friedman number.

4175 has a square comprised of the digits 0-7.

4176 has an 8th root whose decimal part starts with the digits 1-9 in some order.

4180 is the sum of the first 17 Fibonacci numbers.

4181 is the first composite number in the Fibonacci sequence with a prime index.

4183 is a narcissistic number in base 7.

4185 is the smaller number in a Ruth-Aaron pair.

4186 is a hexagonal, 13-gonal, triangular number.

4187 is the smallest Rabin-Miller pseudoprime with an odd reciprocal period.

4188 is a value of n for which σ(n-1) = σ(n+1).

4191 is the number of graphs with 12 vertices and 10 edges.

4192 is the larger number in a Ruth-Aaron pair.

4193 is the number of 3×3 sliding puzzle positions that require exactly 16 moves to solve starting with the hole on a side.

4195 has a sum of prime factors that is equal to the sum of the prime factors of the two preceding numbers.

4199 is the product of 3 consecutive primes.

4200 is divisible by its reverse.

4202 = 42025 + 42027 + 42028.

4204 and the two numbers before it and after it are all products of exactly 3 primes.

4205 has the property that if each digit is replaced by its square, the resulting number is a square.

4207 is the number of cubic graphs with 16 vertices.

4209 is the number of conjugacy classes of the alternating group A32.

4210 is the number of graphs with 10 vertices with clique number 7.

4211 is a number whose product of digits is equal to its sum of digits.

4215 is a centered dodecahedral number.

4216 is an octagonal pyramidal number.

4217 is the smallest number whose 8th power has 29 digits.

4219 is a Cuban prime.

4223 is the maximum number of 12th powers needed to sum to any number.

4224 is a palindrome that is one less than a square.

4225 is the smallest number that can be written as the sum of two squares in 12 ways.

4231 is the number of labeled partially ordered sets with 5 elements.

4232 is the number of different products of subsets of the set {1, 2, 3, ... 16}.

4233 is a heptagonal pyramidal number.

4235 has a cube that contains only digits 5 and larger.

4237 is the number of ordered sequences of coins totaling 30 cents.

4240 is a Leyland number.

4243 = 444 + 22 + 444 + 3333.

4249 is a value of n for which cos(n) is smaller than any previous integer.

4252 is the smallest number in base 8 to have 5 different digits.

4253 is the exponent of a Mersenne prime.

4255 is a centered tetrahedral number.

4258 is the sum of the digits of the 18th Mersenne prime.

4260 is a value of n for which n+1, 2n+1, 3n+1, and 4n+1 are all prime.

4264 is a number whose sum of squares of the divisors is a square.

4267 has a 4th power that is the sum of four 4th powers.

4269 has a cube whose first few digits are 77799797....

4278 does not occur in its factorial in base 2.

4279 is the smallest semiprime super-catalan number..

4280 has a square root whose decimal part starts with the digits 0-9 in some order.

4283 is the smallest number with complexity 29.

4285 is a structured hexagonal diamond number.

4290 is a value of n for which 2nCn is divisible by n2.

4293 has exactly the same digits in 3 different bases.

4294 is a value of n for which σ(n) = φ(n) + φ(n-1) + φ(n-2).

4297 is the smallest prime that is followed by 29 composite numbers.

4300 has the property that if each digit is replaced by its square, the resulting number is a square.

4303 is the number of triangles of any size contained in the triangle of side 25 on a triangular grid.

4305 has exactly the same digits in 3 different bases.

4310 has exactly the same digits in 3 different bases.

4312 is the smallest number whose 10th power starts with 7 identical digits.

4320 = (6+4) × (6+3) × (6+2) × (6+0).

4321 has digits in arithmetic sequence.

4324 is the sum of the first 23 squares.

4325 is a member of the Fibonacci-type sequence starting with 4 and 9.

4329 is the only number n so that n, 2n, 4n, and 6n together contain every digit 1-9 exactly twice.

4332 = 444 + 3333 + 333 + 222.

4333 has a 4th power that is the sum of four 4th powers.

4335 = 444 + 3333 + 3 + 555.

4336 = 4 + 3333 + 333 + 666.

4337 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

4339 = 4 + 3333 + 3 + 999.

4340 is the number of 3×3 sliding puzzle positions that require exactly 27 moves to solve starting with the hole in the center.

4342 appears inside its 4th power.

4343 has the property that the sum of its prime factors is equal to the product of its digits.

4347 is a value of n for which 2n and 5n together use the digits 1-9 exactly once.

4352 has a cube that contains only even digits.

4356 is two thirds of its reverse.

4357 is the smallest number with the property that its first 5 multiples contain the digit 7.

4359 is a perfect totient number.

4364 is a value of n for which σ(n) = σ(n+1).

4365 is a value of n for which 4n and 9n together use each digit exactly once.

4368 = 16C5.

4369 = 1111 in base 16.

4374 and its successor are both divisible by 4th powers.

4375 is a perfect totient number.

4376 and its reverse are both differences of positive cubes.

4381 is a stella octangula number.

4388 divides 11 + 22 + 33 + . . . + 43884388.

4390 is a house number.

4392 is a value of n for which n and 4n together use each digit 1-9 exactly once.

4396 = 157 × 28 and each digit is contained in the equation exactly once.

4402 has the property that if each digit is replaced by its square, the resulting number is a square.

4409 is prime, but changing any digit makes it composite.

4410 is a Padovan number.

4413 is the index of a prime Euclid number.

4418 is the number of 7-nons.

4421 = 7! - 6! + 5! - 4 ! + 3! - 2! + 1!.

4422 is the maximum value of n so that there exist 5 denominations of stamps so that every postage from 1 to n can be paid for with at most 15 stamps.

4423 is the exponent of a Mersenne prime.

4425 is the sum of the first five 5th powers.

4431 is the number of graphs with 8 vertices that have 2 automorphisms.

4434 is the sum of its proper divisors that contain the digit 7.

4435 uses the same digits as φ(4435).

4438 is the number of 15-hexes with reflectional symmetry.

4442 is a value of n for which σ(n) is a repdigit.

4444 is a repdigit.

4445 is the smallest number that can be written as the sum of 4 distinct positive cubes in 4 ways.

4449 has a 4th power that is the sum of four 4th powers.

4455 is the number of permutations of 12 items that fix 8 elements.

4457 is the closest integer to 22e.

4465 + φ(4465) = 7777.

4467 is the number of terms in the 16th derivative of f(f(f(x))).

4473 is a value of n for which σ(n) = 2reverse(n).

4480 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

4481 is a prime that is the average of two 4th powers.

4485 is the number of 3×3 sliding puzzle positions that require exactly 16 moves to solve starting with the hole in a corner.

4488 = 256 + 257 + . . . + 272 = 273 + 274 + . . . + 288.

4489 is a square whose digits are non-decreasing.

4493 is the number of ways to divide a 11×11 grid of points into two sets using a straight line.

4495 = 31C3.

4498 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

4500 is the number of regions formed when all diagonals are drawn in a regular 20-gon.

4503 is the largest number that is not the sum of 4 or fewer squares of composites.

4505 is a Zeisel number.

4506 is the sum of its proper divisors that contain the digit 5.

4510 = 4444 + 55 + 11 + 0.

4511 = 4444 + 55 + 11 + 1.

4512 = 4444 + 55 + 11 + 2.

4513 = 4444 + 55 + 11 + 3.

4514 = 4444 + 55 + 11 + 4.

4515 = 4444 + 55 + 11 + 5.

4516 = 4444 + 55 + 11 + 6.

4517 = 4444 + 55 + 11 + 7.

4518 = 4444 + 55 + 11 + 8.

4519 = 4444 + 55 + 11 + 9.

4520 is the number of regions the complex plane is cut into by drawing lines between all pairs of 20th roots of unity.

4522 is the number of non-intersecting rook paths joining opposite corners of a 8×3 chessboard.

4523 has a square in base 2 that is palindromic.

4524 is the maximum number of pieces a torus can be cut into with 29 cuts.

4526 is the maximum number of regions a cube can be cut into with 30 cuts.

4527 is a value of n for which n and 7n together use each digit 1-9 exactly once.

4530 has the property that the sum of the factorials of its digits is its largest prime factor.

4535 is the number of unlabeled topologies with 7 elements.

4536 is the Stirling number of the first kind s(9,6).

4541 has a square with the first 3 digits the same as the next 3 digits.

4542 is the number of trees on 20 vertices with diameter 5.

4544 is a Kaprekar number for cubes.

4547 is a value of n for which one more than the product of the first n primes is prime.

4548 is the sum of its proper divisors that contain the digit 7.

4550 is the Stirling number of the second kind S(15,13).

4552 has a square with the first 3 digits the same as the next 3 digits.

4556 is the trinomial coefficient T(17,13).

4558 is a member of the Fibonacci-type sequence starting with 1 and 4.

4563 is an Achilles number.

4565 is the number of partitions of 29.

4567 has digits in arithmetic sequence.

4576 is a truncated tetrahedral number.

4579 is an octahedral number.

4582 is the number of partitions of 52 into distinct parts.

4583 is a value of n for which one less than the product of the first n primes is prime.

4589 is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged.

4591 is a value of n for which n and 8n together use each digit 1-9 exactly once.

4600 is a decagonal pyramidal number.

4604 is a value of n for which cos(n) is smaller than any previous integer.

4607 is a Woodall number.

4608 is the number of ways to place 2 non-attacking kings on a 10×10 chessboard.

4609 is a Cullen number.

4610 is a Perrin number.

4613 is the number of graphs with 10 edges.

4614 is the number of ways to stack 27 pennies in contiguous rows so that each penny lies on the table or on two pennies.

4616 has a square comprised of the digits 0-7.

4619 is a value of n for which 4n and 5n together use each digit exactly once.

4620 is the largest order of a permutation of 30 or 31 elements.

4615 is a value of n for which σ(φ(n)) = 2σ(n).

4622 is the number of 12-ominoes that contain 1 hole.

4623 is a value of n for which σ(n) = 2reverse(n).

4624 = 44 + 46 + 42 + 44.

4625 is the number of trees on 16 vertices with diameter 7.

4628 is a Friedman number.

4631 has a cube with only odd digits.

4640 is the number of different score sequences of an 11-team round robin tournament.

4641 is a rhombic dodecahedral number.

4642 is the smallest number whose cube has 11 digits.

4644 is a value of n for which 7n and 9n together use each digit exactly once.

4645 has the property that the concatenation of its prime factors in increasing order is a square.

4647 is a member of the Fibonacci-type sequence starting with 1 and 7.

4649 has a 9th root that starts 2.55555....

4650 is the maximum number of regions space can be divided into by 25 spheres.

4652 is the number of labeled connected graphs with 6 vertices that have chromatic number 4.

4653 is a value of n for which n and 6n together use each digit 1-9 exactly once.

4655 is the number of 10-ominoes.

4657 is a number that does not have any digits in common with its cube.

4663 is the number of 12-ominoes that contain holes.

4665 = 33333 in base 6.

4666 is the number of tilted rectangles with vertices in a 13×13 grid.

4676 is the sum of the first seven 4th powers.

4680 is a value of n for which n, n2, and n3 have the same digit sum.

4681 = 11111 in base 8.

4682 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 14.

4683 is the number of orderings of 6 objects with ties allowed.

4684 is the number of subsets of {1,2,3,...,15} that have a sum divisible by 7.

4685 is the number of anisohedral 15-hexes.

4686 is the denominator of the 70th Bernoulli number.

4687 is a value of n for which σ(φ(n)) = 3σ(n).

4688 is 2-automorphic.

4689 is a value of n for which n and 8n together use each digit 1-9 exactly once.

4691 is a value of n for which n and 8n together use each digit 1-9 exactly once.

4695 are the first 4 digits of 44695.

4697 is a value of n for which φ(n) = φ(reverse(n)).

4698 is the smallest number so that it and its reverse are divisible by 54.

4705 is the sum of consecutive squares in 2 ways.

4709 is the number of symmetric plane partitions of 31.

4713 is a value of n such that the nth Cullen number is prime.

4714 is the smallest number whose square begins with four 2's.

4723 is the index of a prime Fibonacci number.

4725 is an odd abundant number.

4726 is the smallest number whose cube contains 5 consecutive 5's.

4727 is the sum of the squares. of the first 12 primes.

4730 is the number of multigraphs with 5 vertices and 13 edges.

4732 is a number that does not have any digits in common with its cube.

4734 is the sum of its proper divisors that contain the digit 7.

4735 is a value of n for which 4n and 5n together use each digit exactly once.

4738 is a Menage number.

4740 is the trinomial coefficient T(10,3).

4741 is a value of n for which 4n and 5n together use each digit exactly once.

4743 is a value of n for which 2n and 5n together use the digits 1-9 exactly once.

4748 is a value of n for which σ(n) = φ(n) + φ(n-1) + φ(n-2).

4750 is a hexagonal pyramidal number.

4751 is the starting location of 8888 in the decimal expansion of π.

4752 = (4+4) × (4+7) × (4+5) × (4+2).

4755 has a cube whose digits occur with the same frequency.

4757 is the number of ordered partitions of 23 into distinct parts.

4758 does not occur in its factorial in base 2.

4760 is the sum of consecutive squares in 2 ways.

4761 is the number of subsets of {1,2,3,...,15} that have an integer average.

4762 is the smallest number not a power of 10 whose square contains the same digits.

4764 is an hexagonal prism number.

4766 is the number of rooted trees with 12 vertices.

4769 is a value of n for which 4n and 5n together use each digit exactly once.

4776 is a structured pentagonal hexacontahedral number.

4784 has a sum of digits equal to its largest prime factor.

4785 has a square that is the sum of a cube and a 4th power.

4787 is a value of n for which one more than the product of the first n primes is prime.

4788 is a Keith number.

4793 = 4444 + 7 + 9 + 333.

4797 is a cubic star number.

4798 is a value of n for which n!!! + 1 is prime.

4802 can be written as the sum of 2 or 3 positive 4th powers.

4804 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

4807 is the smallest quasi-Carmichael number in base 10.

4815 is the number of ways to stack 33 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

4819 is a tetranacci number.

4823 is the number of triangles of any size contained in the triangle of side 26 on a triangular grid.

4831 is the smallest prime so that it and the next 2 primes all end in 1.

4832 is a number whose square contains the same digits.

4835 is the number of anisohedral 14-hexes.

4843 is a value of n for which σ(φ(n)) = 2σ(n).

4845 = 20C4.

4848 is the number of quaternary square-free words of length 8.

4850 is a Wedderburn-Etherington number.

4851 is a pentagonal pyramidal number.

4852 is the sum of the squares of 4 consecutive primes.

4854 does not occur in its factorial in base 2.

4860 is the order of a perfect group.

4862 is the 9th Catalan number.

4863 is the smallest number that cannot be written as the sum of 273 8th powers.

4866 is the number of partitions of 48 in which no part occurs only once.

4869 is a value of n for which 3n and 8n together use each digit exactly once.

4875 is the number of graphs with 10 vertices and 3 cycles.

4876 divides the sum of the first 681 composite numbers.

4877 is the largest prime factor of 87654321.

4878 is the number of alternating knots with 13 crossings.

4879 = 238 + 0 + 4641 and has the square 23804641.

4890 is a narcissistic number in base 5.

4891 is a narcissistic number in base 5.

4893 is a value of n for which 2n and 7n together use the digits 1-9 exactly once.

4895 is the product of two consecutive Fibonacci numbers.

4896 = 18P3.

4899 is the sum of the squares of 3 consecutive primes.

4900 is the only non-trivial number which is both square and square pyramidal.

4901 has a base 3 representation that begins with its base 7 representation.

4902 is the starting location of 2222 in the decimal expansion of π.

4905 is the sum of all the 2-digit numbers.

4911 has a 9th power whose first few digits are 16616111....

4913 is the cube of the sum of its digits.

4917 is the trinomial coefficient T(11,5).

4919 is a prime that remains prime if any digit is deleted.

4920 = 6666 in base 9.

4922 is a number whose sum of divisors is a 5th power.

4923 and the two numbers before it and after it are all products of exactly 3 primes.

4924 and the two numbers before it and after it are all products of exactly 3 primes.

4927 is a value of n for which 4n and 5n together use each digit exactly once.

4928 is a structured truncated tetrahedral number.

4930 = 66779 = 2A2A12 = 232313 = 101017, each using two digits exactly twice each.

4931 is a value of n for which 2n and 7n together use the digits 1-9 exactly once.

4933 is the number of digits in the 14th Fermat number.

4936 = 4 + 44 + 444 + 4444.

4939 has the property that the concatenation of its prime factors in increasing order is a square.

4941 is a centered cube number.

4944 is a value of n for which n φ(n) is a palindrome.

4949 has a 4th power that is the sum of four 4th powers.

4950 is both a triangular number and 5 times a triangular number.

4952 is the closest integer to 15π.

4959 is a value of n for which cos(n) is smaller than any previous integer.

4960 = 32C3.

4961 is a hexanacci number.

4964 is the number of binary partitions of 42.

4967 is the number of partitions of 49 in which no part occurs only once.

4974 is the sum of its proper divisors that contain the digit 8.

4975 is a value of n for which n!!! + 1 is prime.

4979 is a centered tetrahedral number.

4980 has the same digits as the 4980th prime.

4982 is a number whose sum of divisors is a 5th power.

4985 is the number of graphs with 8 vertices with clique number 4.

4990 is the maximum number of pieces a torus can be cut into with 30 cuts.

4991 is a Lucas-Carmichael number.

4992 is the maximum number of regions a cube can be cut into with 31 cuts.

4993 is a Proth prime.

4995 has a 5th power that is closer to a cube than a square.

4999 is the smallest number whose digits add to 31.

5000 is the largest number whose English name does not repeat any letters.

5001 appears inside its 4th power.

5002 has a 4th power containing only 4 different digits.

5005 is the smallest palindromic product of 4 consecutive primes.

5009 would be prime if preceded and followed by a 1, 3, 7, or 9.

5010 has a square with the last 3 digits the same as the 3 digits before that.

5016 is a heptagonal pyramidal number.

5020 is an amicable number.

5024 is a member of the Fibonacci-type sequence starting with 2 and 7.

5026 is the number of connected graphs with 11 vertices and 1 cycle.

5030 is the closest integer to 23e.

5036 and the two numbers before it and after it are all products of exactly 3 primes.

5039 is the number of planar partitions of 18.

5040 = 7!

5041 is the largest square known of the form n! + 1.

5042 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 13.

5044 is a value of n for which φ(n) and σ(n) are square.

5046 is the first of five consecutive squareful numbers.

5048 is the number of strongly connected digraphs with 5 vertices.

5049 is an octagonal pyramidal number.

5050 is the sum of the first 100 integers.

5054 = 555 + 0 + 55 + 4444.

5055 has exactly the same digits in 3 different bases.

5056 is the number of ways to flip a coin 13 times and get at least 3 heads in a row.

5057 is the number of squares in a 16×16 grid of squares with diagonals drawn.

5059 is the number of inequivalent asymmetric Ferrers graphs with 33 points.

5061 is a number n whose 5th root has a decimal part that begins with the digits of n.

5071 is a Lucas 3-step number and a Lucas 4-step number.

5069 is the number of square-free graphs with 10 vertices.

5078 is the number of rectangles with corners on an 12×12 grid of points.

5080 is a structured truncated octahedral number.

5083 is an centered icosahedral number.

5084 is the number of inequivalent Ferrers graphs with 33 points.

5087 has an eleventh root whose decimal part starts with the digits 1-9 in some order.

5088 divides the sum of the digits of 25088 × 5088!.

5096 is the number of possible rook moves on a 14×14 chessboard.

5098 is the number of 3-valent trees with 17 vertices.

5100 is divisible by its reverse.

5103 and its successor are both divisible by 4th powers.

5104 is the smallest number that can be written as the sum of 3 cubes in 3 ways.

5105 would be prime if preceded and followed by a 1, 3, 7, or 9.

5107 preceded by 5107 1's is prime.

5108 is the number of different flushes in 5 card poker.

5109 is the number of conjugacy classes of the alternating group A33.

5118 is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps.

5120 is the number of edges in a 10 dimensional hypercube.

5130 is a value of n for which φ(n) and σ(n) are square.

5133 is the smallest integer ratio of a 18-digit number to its product of digits.

5135 has the property that the sum of the factorials of its digits is its largest prime factor.

5135 is not the sum of a square, a cube, a 4th power, and a 5th power.

5136 does not occur in its factorial in base 2.

5141 is the only four digit number that is reversed in hexadecimal.

5142 is the sum of its proper divisors that contain the digit 7.

5143 = 555 + 111 + 4444 + 33.

5146 has a base 3 representation that begins with its base 7 representation.

5152 is the number of legal rook moves in Chess.

5153 is an Eisenstein-Mersenne prime.

5160 is a hendecagonal pyramidal number.

5161 = 5! + (1+6)! + 1!

5162 = 5! + (1+6)! + 2.

5163 = 5! + (1+6)! + 3.

5164 = 5! + (1+6)! + 4.

5165 = 5! + (1+6)! + 5.

5166 = 5! + (1+6)! + 6.

5167 = 5! + (1+6)! + 7.

5168 has a square root that has four 8's immediately after the decimal point.

5169 = 5! + (1+6)! + 9.

5172 has a cube whose last few digits are ...48848448.

5174 has a 4th power containing only 4 different digits.

5177 is the number of labeled graphs with 6 vertices that have chromatic number 2.

5177 is the number of labeled bipartite graphs with 6 vertices.

5180 is the smallest number whose 7th power has 26 digits.

5181 is a structured octagonal anti-diamond number.

5182 is a number whose sum of divisors is a 5th power.

5183 is the product of twin primes.

5184 is the number of ways to place 2 non-attacking rooks on a 9×9 chessboard.

5185 is the number of 2×2 singular matrices mod 17.

5186 is equal to the sum of its anti-divisors.

5187 is the only number n known for which φ(n-1) = φ(n) = φ(n+1).

5191 is a value of n for which σ(n+1) = 2σ(n).

5199 divides the sum of the cubes of the first 5199 primes.

5200 is divisible by its reverse.

5204 has the property that if each digit is replaced by its square, the resulting number is a square.

5211 has a square root whose decimal part starts with the digits 1-9 in some order.

5216 is a structured hexagonal diamond number.

5218 is the number of 3-colorable graphs connected graphs with 8 vertices.

5220 = 1111 in base 17.

5225 is the number of ways to color the vertices of a triangle with 25 colors, up to rotation.

5226 is the number of ways to color the vertices of a square with 12 colors, up to rotation.

5229 uses the same digits as φ(5229).

5234 has a cube that is only 17 away from a square.

5237 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5241 is the starting location of 7777 in the decimal expansion of π.

5242 is the number of ways to place 8 non-attacking kings on a 8×8 chessboard so that there is a king in every row and column.

5244 is the sum of consecutive squares in 2 ways.

5247 is the number of ordered ways to write 1 as a sum of reciprocals of integers no larger than 10.

5248 is the number of ordered ways to write 1 as a sum of reciprocals of integers no larger than 11.

5250 is the number of linear geometries on 10 unlabeled points.

5252 is the maximum number of regions space can be divided into by 26 spheres.

5256 is the number of labeled partially ordered sets of 4 elements.

5257 is a member of the Fibonacci-type sequence starting with 1 and 8.

5258 has a base 8 representation which is the reverse of its base 7 representation.

5260 is the number of multigraphs with 24 vertices and 4 edges.

5264 is the smallest number so that it and its successor are both the product of 2 primes and the 4th power of a prime.

5265 is a Rhonda number.

5269 is the number of binary rooted trees with 18 vertices.

5271 is a value of n for which 2n and 7n together use each digit exactly once.

5274 is the sum of its proper divisors that contain the digit 7.

5278 is the number of ways, up to symmetry, to pick 3 elements of an 8×8 grid.

5279 is the number permutations of {1,2,3,...,20} where adjacent numbers differ by no more than 2.

5281 has a 4th power that is the sum of four 4th powers.

5282 is the number of different arrangements (up to rotation and reflection) of 8 non-attacking rooks on a 8×8 chessboard.

5284 and the two numbers before it and after it are all products of exactly 3 primes.

5289 is a structured rhombic triacontahedral number.

5291 is a value of n for which n(n+1) is a palindrome.

5292 = 28 + 0 + 0 + 5264 and has square 28005264.

5293 is the smallest number that ends an arithmetic progression of 12 numbers with the same prime signature.

5296 is the Entringer number E(8,3).

5306 is the smallest number whose 9th power starts with 4 identical digits.

5309 has the property that if each digit is replaced by its square, the resulting number is a square.

5312 is the index of a prime Woodall number.

5313 is the index of a triangular number containing only 3 different digits.

5314 is a value of n for which cos(n) is smaller than any previous integer.

5322 is the starting location of 7777 in the decimal expansion of π.

5324 is the number of binary cube-free words of length 20.

5327 is a value of n for which 2n and 7n together use each digit exactly once.

5328 is the number of one-sided 6-knights.

5332 is a Kaprekar constant in base 3.

5335 is the magic constant of a 22×22 magic square.

5336 is a house number.

5340 is an octahedral number.

5346 = 198 × 27 and each digit is contained in the equation exactly once.

5349 = 12345 in base 8.

5355 is an odd primitive abundant number.

5357 is the smallest number that can not be formed using the digit 1 at most 27 times, together with the symbols +, –, × and ÷.

5358 are the first 8 digits of π5358.

5362 is the number of Chess positions that can be reached after 2 moves by white and 1 move by black.

5364 is a value of n for which 3n and 7n together use each digit exactly once.

5366 is the number of graphs with 8 vertices that have chromatic number 4.

5367 uses the same digits as φ(5367).

5369 is a Wolstenholme number.

5371 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5376 is the order of a perfect group.

5382 is the number of non-intersecting rook paths joining opposite corners of a 6×4 chessboard.

5383 is the number of triangles of any size contained in the triangle of side 27 on a triangular grid.

5387 is the index of a prime Fibonacci number.

5390 is the number of ways to 7-color the faces of a cube.

5392 is a Leyland number.

5399 has a cube whose digits occur with the same frequency.

5400 is divisible by its reverse.

5401 is a member of the Fibonacci-type sequence starting with 3 and 7.

5405 is the smaller number in a Ruth-Aaron pair.

5406 is the number of ways a 9×1 rectangle can be surrounded by 9×1 rectangles.

5408 is an Achilles number.

5409 and its reverse are both differences of positive cubes.

5412 is a value of n so that n(n+4) is a palindrome.

5414 is the number of binary partitions of 43.

5418 is a value of n for which n and 7n together use each digit 1-9 exactly once.

5419 is a Cuban prime.

5422 is the number of semigroups of order 6 with 3 idempotents.

5431 is the smallest number whose 4th power contains 5 consecutive 9's.

5432 has digits in arithmetic sequence.

5434 is the sum of consecutive squares in 2 ways.

5436 is the number of terms in the 10th derivative of f(f(f(f(f(x))))).

5439 is a Rhonda number.

5440 is the number of ways to legally add 2 sets of parentheses to a product of 15 variables.

5443 is the smallest prime p with 17 consecutive quadratic residues mod p.

5446 is the number of ways to to arrange the numbers 1-10 around a circle so that the sums of adjacent numbers are distinct.

5448 is the number of ways to cut a 10×10 chessboard into 2 pieces with equal areas with a cut that only travels up and right.

5455 is a Kaprekar number for cubes.

5456 and its reverse are tetrahedral numbers.

5457 is a number whose sum of divisors is a 5th power.

5460 is both a triangular number and 7 times a triangular number.

5461 is an Euler pseudoprime.

5462 is the number of ways to walk along 14 edges of a triangle and end at the original vertex.

5463 has a 4th power that is the sum of four 4th powers.

5464 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 12.

5469 has the property that e5469 is within .00003 of an integer.

5471 contains no 0's in base 3 through base 10.

5472 has a base 3 representation that ends with its base 4 representation.

5473 has a base 3 representation that ends with its base 4 representation.

5474 is a stella octangula number.

5477 and its reverse are both one more than a square.

5478 is the number of graphs with 10 vertices that have chromatic number 2.

5479 is the number of bipartite graphs with 10 vertices.

5482 is the number of 3×3 sliding puzzle positions that require exactly 16 moves to solve starting with the hole in the center.

5483 is the number of unlabeled distributive lattices with 18 elements.

5487 is the maximum number of pieces a torus can be cut into with 31 cuts.

5488 is an Achilles number.

5489 is the maximum number of regions a cube can be cut into with 32 cuts.

5491 has a 4th power that is the sum of four 4th powers.

5493 is the number of integers with complexity 30.

5499 is the average of all the even 4-digit numbers.

5504 is the number of series-parallel networks with 6 labeled edges.

5505 is a value of n for which n!!! - 1 is prime.

5507 has a square root whose decimal part starts with the digits 0-9 in some order.

5508 is the generalized Catalan number C(13,5).

5509 is the number of multigraphs with 8 vertices and 9 edges.

5513 is the number of self-avoiding walks of length 10.

5525 is the smallest number that can be written as the sum of 2 squares in 6 ways.

5530 is a hexagonal pyramidal number.

5533 is the number of graphs with 10 vertices and 2 cycles.

5536 is the 16th tetranacci number.

5542 is the number of anisohedral 19-ominoes.

5543 has a 4th power that is the sum of four 4th powers.

5544 is the number of permutations of 9 items that fix 4 elements.

5545 is a member of the Fibonacci-type sequence starting with 1 and 5.

5551 is the number of trees on 17 vertices with diameter 6.

5554 is a Kaprekar number for cubes.

5555 is a repdigit.

5557 contains no 0's in base 3 through base 10.

5560 are the first 4 digits of 75560.

5561 has the property that the sum of its prime factors is equal to the product of its digits.

5564 is an amicable number.

5565 is a doubly triangular numbers.

5566 is a pentagonal pyramidal number.

5568 is the number of ways to put 8 checkers on an 8×8 checkerboard so that each row, column, and main diagonal contains exactly one checker.

5571 is a perfect totient number.

5573 is the number of digits in the 6th Cullen prime.

5576 is a decagonal pyramidal number.

5585 is the number of monoids of order 7 with 2 idempotents.

5586 does not occur in its factorial in base 2.

5587 has a 5th root that starts 5.61611166....

5588 is the index of a triangular number containing only 3 different digits.

5591 is the smallest prime that is followed by 31 composite numbers.

5594 is the number of ways to dissect a 14-gon using non-crossing diagonals into polygons with an even number of sides.

5595 is the number of labeled mappings from 6 points to themselves with exactly 3 cycles.

5597 has a cube with only odd digits.

5600 is the number of self-complementary graphs with 13 vertices.

5602 = 22222 in base 7.

5604 is the number of partitions of 30.

5610 is divisible by its reverse.

5611 is the smallest number for which it and the 3 numbers before and after it all have φ(n) divisible by 10.

5612 has the property that dropping its first and last digits gives its largest prime factor.

5616 is the order of a non-cyclic simple group.

5617 is a divisor of the sum of the 4th powers of its divisors.

5619 has a cube that contains the digits 5619 in reverse order.

5620 is the smallest composite number which remains composite when preceded or followed by any digit.

5623 and the primes preceding it and following it are all equal to 7 (mod 16).

5624 is the smallest number whose 4th power has 15 digits.

5625 has a cube that is the sum of 3 positive cubes.

5629 is the maximum value of n so that there exist 5 denominations of stamps so that every postage from 1 to n can be paid for with at most 16 stamps.

5637 uses the same digits as φ(5637).

5638 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole in a corner.

5647 is the closest integer to 24e.

5651 is a number n for which n, n+2, n+6, and n+8 are all prime.

5661 is the trinomial coefficient T(18,14).

5664 is a Rhonda number.

5668 is the number of semigroups of order 6 with 5 idempotents.

5669 is a value of n for which cos(n) is smaller than any previous integer.

5670 is a value of n for which φ(n) and σ(n) are square.

5671 is a triangular number that is the product of two primes.

5673 is the smallest number whose 6th power starts with 5 identical digits.

5675 is the number of monic polynomials of degree 13 with integer coefficients whose complex roots are all in the unit disk.

5678 has digits in arithmetic sequence.

5679 is the number of drawings of the complete graph K10 with a minimal number of crossings.

5682 is the sum of its proper divisors that contain the digit 4.

5689 is the largest 4-digit prime with strictly increasing digits.

5691 is the number of different resistances that can be created in a circuit of 11 equal resistors.

5692 is a number that does not have any digits in common with its cube.

5693 = 5555 + 6 + 99 + 33.

5694 = 17082 / 3, and each digit is contained in the equation exactly once.

5696 is the smallest number whose square contains 4 consecutive 4's.

5697 has a 21st power that contains five 5's, six 6's, nine 9's, and seven 7's.

5698 is the smallest number whose 8th power starts with 5 identical digits.

5700 is divisible by its reverse.

5709 is a structured pentakis dodecahedral number.

5711 is the smallest prime p with 18 consecutive quadratic residues mod p.

5712 is the number of Gray codes for a 4-dimensional cube.

5717 is a value of n for which the first n binary digits of π form a prime.

5718 is the number of partitions of 54 into distinct parts.

5719 is a Zeisel number.

5720 is a dodecagonal pyramidal number.

5721 is the number of graphs with 8 vertices that have chromatic number 3.

5723 has the property that its square starts with its reverse.

5729 has a 4th power that is the sum of four 4th powers.

5731 is a value of n for which n (n+2) is a palindrome.

5734 has a square that is a centered pentagonal number.

5737 is the smallest number that can not be formed using the digit 1 at most 22 times, together with the symbols +, × and ^.

5739 is a value of n for which 5n and 7n together use each digit exactly once.

5740 = 7777 in base 9.

5741 is the 11th Pell number.

5742 is a value of n for which 5n and 8n together use each digit exactly once.

5751 is the number of ordered sequences of coins totaling 31 cents.

5754 is the number of ways a loop can cross two parallel lines a total of 12 times.

5755 is the sum of the digits of the 19th Mersenne prime.

5760 is the order of a perfect group.

5767 is the product of two consecutive primes.

5768 is the 16th tribonacci number.

5770 is a value of n for which φ(n) and σ(n) are square.

5772 are the first 4 decimal digits of Euler's constant.

5773 is the index of a triangular number containing only 3 different digits.

5774 is the smallest number whose square begins with four 3's.

5775 is the smallest value of n for which both n and n+1 are abundant.

5776 is the square of the last half of its digits.

5777 is the smallest multi-digit number which is not the sum of a prime and twice a square.

5778 is the largest Lucas number which is also a triangular number.

5781 is a centered tetrahedral number.

5784 = 555 + 777 + 8 + 4444.

5786 = 5555 + 77 + 88 + 66.

5789 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5790 has the same digits as the 5790th prime.

5791 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5793 are the first 4 digits of 5793e.

5795 is a value of n such that the nth Cullen number is prime.

5796 = 138 × 42 and each digit is contained in the equation exactly once.

5798 is the 11th Motzkin number.

5807 is the index of a Wagstaff prime.

5813 is the concatenation of 3 consecutive Fibonacci numbers.

5814 = 19P3.

5817 = 34902 / 6, and each digit is contained in the equation exactly once.

5818 contains no 0's in base 3 through base 10.

5819 has a sum of digits equal to its largest prime factor.

5821 contains no 0's in base 3 through base 10.

5822 is the number of conjugacy classes in the automorphism group of the 16 dimensional hypercube.

5823 is the smallest value of n for which n and 3n together use each digit 1-9 exactly once.

5824 can be written as the difference between two positive cubes in more than one way.

5825 are the first 4 digits of e5825.

5830 is a weird number.

5831 has a sum of digits equal to its largest prime factor.

5832 is a value of n for which n and 3n together use each digit 1-9 exactly once.

5834 is the number of digits of the 21st perfect number.

5839 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5842 is a Padovan number.

5843 has a 5th root that starts 5.66666....

5844 is the number of ways to stack 34 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

5848 has a square that remains square when a 9 is appended to it.

5850 is a value of n for which n-1 and n+1 are twin primes, and so are 2n-1 and 2n+1.

5851 is a value of n for which n, n2, and n3 have the same digit sum.

5853 is the index of a triangular number containing only 3 different digits.

5856 = 1 × 6 × 16 × 61.

5859 can be written as the difference between two positive cubes in more than one way.

5860 is the sum of the squares of 4 consecutive primes.

5863 is the starting location of 7777 in the decimal expansion of π.

5864 has a 14th power that contains five 5's, eight 8's, six 6's, and four 4's.

5865 is an enneagonal pyramidal number.

5867 is a member of the Fibonacci-type sequence starting with 1 and 9.

5868 is a value of n for which n, n2, and n3 have the same digit sum.

5870 has a digit sum smaller than its cube.

5872 = 5555 + 88 + 7 + 222.

5873 divides 11 + 22 + 33 + . . . + 58735873.

5876 is the number of ways to color the vertices of a triangle with 26 colors, up to rotation.

5877 is a value of n for which 5n and 8n, or 8n and 9n, together use each digit exactly once.

5879 is the smallest number so that it and the next 10 numbers all have an odd number of prime factors.

5880 is the Stirling number of the second kind S(10,7).

5885 is a number whose sum of divisors is a 5th power.

5886 is a value of n for which 3n and 5n together use each digit exactly once.

5890 is a heptagonal pyramidal number.

5892 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5895 is the number of necklaces possible with 7 beads, each being one of 5 colors.

5896 is the number of ways to tile a 3×24 rectangle with 3×1 rectangles.

5900 is the number of ways to place 32 points on a 16×16 grid so that no 3 points are on a line.

5904 has a square comprised of the digits 1-8.

5906 is the smallest number which is the sum of 2 rational 4th powers but is not the sum of two integer 4th powers.

5909 is the number of symmetric plane partitions of 32.

5913 = 1! + 2! + 3! + 4! + 5! + 6! + 7!

5914 = 0! + 1! + 2! + 3! + 4! + 5! + 6! + 7!

5915 is the sum of consecutive squares in 2 ways.

5916 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5921 is a value of n for which n and 8n together use each digit 1-9 exactly once.

5923 is the largest n so that Q(√n) has class number 7.

5925 is the index of a triangular number containing only 3 different digits.

5926 + φ(5926) = 8888.

5929 is a square which is also the sum of 11 consecutive squares.

5931 is the number of one-sided 7-kings.

5934 is a value of n for which 5n and 7n together use each digit exactly once.

5936 is divisible by the digits it does not contain, and not divisible by the digits it contains.

5938 is the number of binary partitions of 44.

5939 is the smallest prime so that it and the next 2 primes are all equal to 3 (mod 7).

5940 is divisible by its reverse.

5943 is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors.

5950 is the sum of the digits of the 20th Mersenne prime.

5953 and the primes preceding it and following it are all equal to 3 (mod 14).

5958 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 11.

5959 is the smaller number in a Ruth-Aaron pair.

5960 is the larger number in a Ruth-Aaron pair.

5963 is the number of intersections when all the diagonals of a regular 22-gon are drawn.

5967 is a value of n for which 6n and 7n together use each digit exactly once.

5968 has a square which uses the digits 0-7 each exactly once.

5972 is the smallest number that appears in its factorial 8 times.

5974 is the number of connected planar graphs with 8 vertices.

5975 is a value of n for which σ(n) = σ(reverse(n)).

5976 is a value of n for which n and 7n together use each digit 1-9 exactly once.

5978 is a value of n where φ(n) is the product of the digits of n.

5984 = 34C3.

5985 = 21C4.

5986 and its prime factors contain every digit from 1-9 exactly once.

5993 is the largest number known which is not the sum of a prime and twice a square.

5994 is the number of lattices on 10 unlabeled nodes.

5995 is a palindromic triangular number.

5996 is a truncated tetrahedral number.

5999 is the smallest number whose digits add to 32.

6000 is the number of subsets of the 24th roots of unity that add to 1.

6001 has a cube that is a concatenation of other cubes.

6002 is the number of digits of the 24th Mersenne prime.

6003 has a square with the first 3 digits the same as the next 3 digits.

6006 is the number of intersections when all the diagonals of a regular 21-gon are drawn.

6008 = 14C6 + 14C0 + 14C0 + 14C8.

6009 is a strobogrammatic number.

6011 is a member of the Fibonacci-type sequence starting with 3 and 8.

6012 has a square with the last 3 digits the same as the 3 digits before that.

6014 has a square that is formed by 3 squares that overlap by 1 digit.

6016 is the maximum number of pieces a torus can be cut into with 32 cuts.

6017 is a centered octahedral number.

6018 is the maximum number of regions a cube can be cut into with 33 cuts.

6020 is the number of Hamiltonian graphs with 8 vertices.

6021 has a square that is formed by 3 squares that overlap by 1 digit.

6024 is a value of n for which cos(n) is smaller than any previous integer.

6025 are the last 4 digits of the sum of the first 6025 squares.

6032 is the number of ways to place 2 non-attacking knights on a 9×9 chessboard.

6035 is a number whose sum of divisors is a 5th power.

6040 is the number of ways to divide 6 couples into pairs where no pair is a couple.

6048 is the order of a non-cyclic simple group.

6050 has a sum of digits equal to its largest prime factor.

6058 is a number that does not have any digits in common with its cube.

6065 is the closest integer to 16π.

6070 is a structured truncated tetrahedral number.

6072 is the order of a non-cyclic simple group.

6073 is the order of a non-cyclic simple group.

6075 is an Achilles number.

6077 has a square with the last 3 digits the same as the 3 digits before that.

6080 is the smallest number n>1 whose base 14 representation is equal to φ(n).

6081 has a cube that is the sum of 3 positive cubes.

6083 has a square that is the sum of a cube and a 4th power.

6084 is the number of square-free numbers with 4 or fewer digits.

6084 is the sum of the first 12 cubes.

6092 is the number of 16-ominoes with a line of symmetry.

6093 is a value of n for which 3n and 5n together use each digit exactly once.

6095 is a rhombic dodecahedral number.

6097 is an hexagonal prism number.

6099 concatenated with its successor is square.

6100 has the property that if each digit is replaced by its square, the resulting number is a square.

6102 is the largest number n known where φ(n) is the reverse of n.

6105 is a Huay rhombic dodecahedral number.

6106 is a value of n for which 2φ(n) = φ(n+1).

6107 is a Perrin number.

6111 is a value of n for which σ(n-1) = σ(n+1).

6119 is a strobogrammatic number.

6120 is a highly abundant number.

6121 is the smallest number whose cube contains 4 consecutive 3's.

6128 is a betrothed number.

6137 is a centered dodecahedral number.

6138 is the number of quasi-tetrominoes that fit inside a 7×7 grid.

6141 is a Kaprekar constant in base 2.

6142 is the number of inequivalent asymmetric Ferrers graphs with 34 points.

6143 is the smallest prime that contains twelve 1's in binary.

6144 = 16!!!!.

6145 is a Friedman number.

6155 is a member of the Fibonacci-type sequence starting with 2 and 5.

6164 is the number of 11-ominoes that tile the plane using 180 degree rotations.

.

6167 has a 4th power that is the sum of four 4th powers.

6168 is the number of inequivalent Ferrers graphs with 34 points.

6170 = 5 + 55 + 555 + 5555.

6171 has the property that dropping its first and last digits gives its largest prime factor.

6173 is a prime that remains prime if any digit is deleted.

6174 is the Kaprekar constant for 4-digit numbers.

6175 is the number of regions formed when all diagonals are drawn in a regular 21-gon.

6176 is the last 4-digit sequence to appear in the decimal expansion of π.

6179 is a value of n for which 4n and 5n together use each digit exactly once.

6180 is the smallest number n with φ(n) = 2 reverse(n).

6181 is an octahedral number.

6188 = 17C5.

6189 is the number of ways to write 17 as an ordered sum of positive integers, where adjacent numbers are different.

6194 is the number of ways to place a non-attacking white and black pawn on a 10×10 chessboard.

6196 is the number of regions the complex plane is cut into by drawing lines between all pairs of 21st roots of unity.

6197 is a narcissistic number in base 6.

6200 is a harmonic divisor number.

6201 is the sum of the first 26 squares.

6210 is the number of 5×5 matrices with non-negative entries with every row and column adding to 2.

6211 is a Cuban prime.

6216 has a square with the first 3 digits the same as the next 3 digits.

6219 is a value of n for which 4n and 5n together use each digit exactly once.

6220 = 44444 in base 6.

6221 = 666 + 2222 + 2222 + 1111.

6222 is the smallest number that can not be written as the sum of 2 triangular numbers and a power of 2.

6223 = 666 + 2222 + 2 + 3333.

6224 is the number of permutations of 8 elements have 4th power equal to the identity element.

6225 = 666 + 2 + 2 + 5555.

6232 is an amicable number.

6237 is a number whose sum of the squares of its divisors is a square.

6239, followed by 6239 7's, is prime.

6240 is a highly abundant number.

6244 is a member of the Fibonacci-type sequence starting with 2 and 9.

6245 is the smallest number whose square contains 4 consecutive internal 0's.

6248 is the smallest number with the property that its first 8 multiples contain the digit 4.

6249 is the smallest number with the property that its first 10 multiples contain the digit 4.

6250 is a Leyland number.

6256 is a hendecagonal pyramidal number.

6257 is the number of essentially different ways to dissect a 20-gon into 9 quadrilaterals.

6266 is a truncated octahedral number.

6267 is the number of 15-iamonds with holes.

6270 is a value of n for which n-1 and n+1 are twin primes, and so are 2n-1 and 2n+1.

6271 is the smallest number requiring an addition chain of length 17.

6272 is the number of ways to tile a 4×29 rectangle with 4×1 rectangles.

6273 is the number of ways to 9-color the vertices of a pentagon, up to rotations and reflections.

6274 has a cube whose digits occur with the same frequency.

6276 is a value of n for which φ(n) = φ(reverse(n)).

6279 is the number of subsequences of {1,2,3,...14} in which every odd number has an even neighbor.

6280 has a sum of prime factors that is equal to the sum of the prime factors of the two preceding numbers.

6290 is the number of 13-iamonds that do not tile the plane.

6293 is the number of ordered partitions of 24 into distinct parts.

6296 has a square with the first 3 digits the same as the next 3 digits.

6297 is a value of n for which n and 5n together use each digit 1-9 exactly once.

6299 is the smallest number with complexity 30.

6300 is divisible by its reverse.

6307 is the largest n so that Q(√n) has class number 8.

6309 is the closest integer to 25e.

6310 is the smallest number whose 5th power has 19 digits.

6312 is the sum of its proper divisors that contain the digit 5.

6318 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

6320 is the Entringer number E(8,4).

6322 is the number of idempotent functions from a set of 7 elements into itself.

6327 = 324 + 325 + . . . + 342 = 343 + 344 + . . . + 360.

6331 has the same digits as the 6331st prime.

6336 is the number of ways to tile a 9×4 rectangle with 2×1 rectangles.

6343 is the number of quasi-triominoes that fit inside a 14×14 grid.

6347 has the same digits as the 6347th prime.

6348 is a pentagonal pyramidal number.

6351 is the largest number known that is not the sum of 3 squares or cubes.

6354 is the number of 14-iamonds that tile the plane.

6360 is a value of n for which n-1 and n+1 are twin primes, and so are 3n-1 and 3n+1.

6368 is an amicable number.

6371 has a square that is the sum of 2 relatively prime cubes.

6374 is a value of n for which 4n and 5n together use each digit exactly once.

6375 has a square with the first 3 digits the same as the next 3 digits.

6378 is the number of partitions of 55 into distinct parts.

6379 is a value of n for which cos(n) is smaller than any previous integer.

6380 is a value of n for which n! + 1 is prime.

6381 is the smallest value of n for which n and 9n together use each digit 1-9 exactly once.

6384 is an icosahedral number.

6385 is the number of ways to stack 18 pennies in a line so that each penny lies on the table or on two pennies.

6389 is the number of functional graphs on 11 vertices.

6391 is a hexagonal pyramidal number.

6395 is the number of ways to divide a 12×12 grid of points into two sets using a straight line.

6396 is a divisor of the sum of the 4th powers of its divisors.

6397 has the same digits as the 6397th prime.

6399 and its successor are both divisible by 4th powers.

6400 is a square whose digits are non-increasing.

6403 has a square with the first 3 digits the same as the last 3 digits.

6404 is a value of n for which n!! - 1 is prime.

6406 is the number of permutations of 8 elements where every cycle has equal length.

6408 is the sum of the squares. of the first 13 primes.

6409 is a house number.

6411 is a truncated cube number.

6424 is the number of minimal covers of a set containing 6 elements.

6427 is the number of ways a 6×6 square can be tiled with 1×1 and 2×2 squares.

6432 has the same digits as the 6432nd prime.

6435 = 15C7.

6443 has a cube whose digits occur with the same frequency.

6444 is the smallest number whose 5th power starts with 5 identical digits.

6445, followed by 6445 1's, is prime.

6454 is the smallest value of n for which π(10n) = n.

6455 is the smallest value of n for which the nth prime begins with the digits of n.

6456 is a value of n for which the nth prime begins with the digits of n.

6457 is a value of n for which the nth prime begins with the digits of n.

6458 would be prime if preceded and followed by a 1, 3, 7, or 9.

6459 is a value of n for which the nth prime begins with the digits of n.

6460 is a value of n for which the nth prime begins with the digits of n.

6462 divides the sum of the digits of 6462!.

6466 is the largest known value of n for which the nth prime begins with the digits of n.

6471 is a value of n for which n and 9n together use each digit 1-9 exactly once.

6472 is the number of polyominoes with 9 or fewer squares.

6475 is a value of n for which π(n) is the product of the digits of n.

6479 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6481 = (312 + 1) / (34 + 1).

6487 is the number of partitions of 51 in which no part occurs only once.

6488 would be prime if preceded and followed by a 1, 3, 7, or 9.

6489 is half again as large as the sum of its proper divisors.

6498 is the index of a triangular number containing only 3 different digits.

6500 is a number n whose sum of the factorials of its digits is equal to π(n).

6501 has a square whose reverse is also a square.

6505 is the number of 9-hexes without holes.

6506 is a value of n for which the first n binary digits of π form a prime.

6510 is a number n whose sum of the factorials of its digits is equal to π(n).

6511 is a number n whose sum of the factorials of its digits is equal to π(n).

6514 is the sum of the 4th powers of the digits of the sum of the 4th powers of the digits of itself.

6517 has a sum of digits equal to its largest prime factor.

6521 is a number n whose sum of the factorials of its digits is equal to π(n).

6523 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

6524 has the property that its square starts with its reverse.

6525 is a centered icosahedral number.

6526 is the smallest number whose 10th power contains exactly the same digits as another 10th power.

6527 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

6529 is a Proth prime.

6532 is a member of the Fibonacci-type sequence starting with 1 and 6.

6533 is the number of digits of the 25th Mersenne prime.

6534 is a value of n for which 3n and 7n together use each digit exactly once.

6537 is the smallest value of n for which the numbers n-6 through n+6 can not be written as the sum of 2 squares.

6540 is the number of terms in the 17th derivative of f(f(f(x))).

6543 has a square root that has four 8's immediately after the decimal point.

6544 is a number n whose 9th root has a decimal part that begins with the digits of n.

6545 and its reverse are tetrahedral numbers.

6547 is the number of binary 4×4 matrices with no row or column containing 3 consecutive 1's.

6552 is the number of different full houses in 5 card poker with one joker.

6553 is a Lucas 5-step number.

6556 is the largest palindrome that can be made using 5 digits and the 4 arithmetic operations.

6557 is the product of two consecutive primes.

6560 is the smallest number n where n and n+1 are both products of 7 or more primes.

6561 = 38.

6569 is a value of n for which one less than the product of the first n primes is prime.

6572 is the number of 9-hexes.

6576 = (6! - 6) + (5! - 5) + (7! - 7) + (6! - 6).

6578 is the smallest number which can be written as the sum of three 4th powers in 2 ways.

6579 is the number of ways to color the vertices of a triangle with 27 colors, up to rotation.

6580 is the maximum number of regions a cube can be cut into with 34 cuts.

6581 has the same digits as the 6581st prime.

6583 is a value of n for which σ(φ(n)) = 2σ(n).

6588 is the number of sided 12-iamonds.

6593 = 6 + 5555 + 999 + 33.

6594 is a value of n for which 5n and 7n together use each digit exactly once.

6596 has a square comprised of the digits 0-7.

6601 is a Carmichael number.

6603 is a number whose square and cube use different digits.

6608 is the maximum number of regions space can be divided into by 28 spheres.

6609 has a 4th power that is the sum of four 4th powers.

6611 is a value of n such that the nth Cullen number is prime.

6615 is an odd abundant number.

6620 is the number of 11-ominoes that tile the plane.

6623 has the property that the sum of its prime factors is equal to the product of its digits.

6630 is the number of triangles of any size contained in the triangle of side 29 on a triangular grid.

6636 has exactly the same digits in 3 different bases.

6639 divides 11 + 22 + 33 + . . . + 66396639.

6642 can be written as the sum of 2 or 4 positive 4th powers.

6643 is the smallest number which is palindromic in bases 2 and 3.

6647 has a sum of digits equal to its largest prime factor.

6651 is the index of a triangular number containing only 3 different digits.

6653, when concatenated with 4 less than itself, is square.

6654 is the smallest number whose decimal part of its 4th root starts with the digits 0-9 in some order.

6663 is a value of n for which σ(n) is a repdigit.

6665 is a centered tetrahedral number.

6666 is a repdigit.

6667 is the number of self-dual planar graphs with 24 edges.

6668 is the number of trees on 21 vertices with diameter 5.

6669 is the sum of 3 consecutive cubes.

6680 = 6666 + 6 + 8 + 0.

6681 = 6666 + 6 + 8 + 1.

6682 = 6666 + 6 + 8 + 2.

6683 = 6666 + 6 + 8 + 3.

6684 = 6666 + 6 + 8 + 4.

6685 = 6666 + 6 + 8 + 5.

6686 = 6666 + 6 + 8 + 6.

6687 = 6666 + 6 + 8 + 7.

6688 = 6666 + 6 + 8 + 8.

6689 = 6666 + 6 + 8 + 9.

6694 is a value of n for which the sum of the first n primes is square.

6699 is a strobogrammatic number.

6700 has a cube that contains the digits 6700 in reverse order.

6704 is the number of rooted 8-hexes.

6706 is the number of Hamiltonian paths in a 8×5 rectangle graph.

6712 is the index of a triangular number containing only 3 different digits.

6714 is the index of a triangular number containing only 3 different digits.

6716 is the 4-digit string that appears latest in the decimal expansion of π.

6720 = 8P5.

6721 is a composite value of n that divides the (n-1)st Fibonacci number.

6723 is a value of n for which 3n and 8n together use each digit exactly once.

6726 is the 10th Pell-Lucas number.

6728 is the number of domino tilings of a 6×6 square.

6729 is the smallest value of n for which n and 2n together use each digit 1-9 exactly once.

6731 would be prime if preceded and followed by a 1, 3, 7, or 9.

6732 is a value of n for which 2nCn is divisible by n2.

6734 is a value of n for which cos(n) is smaller than any previous integer.

6735 is a stella octangula number.

6736 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole in the center.

6740 is the number of 13-iamonds that do not tile the plane.

6741 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6742 has a square where the first 6 digits alternate.

6743 is the number of binary 4×5 matrices with no consecutive 1's in any row or column.

6745 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 25 stamps.

6751 is the number of digits of the 23rd perfect number.

6754 is the smallest number in base 9 to have 5 different digits.

6756 has a cube that is the sum of 3 positive cubes.

6759 is the number of graphs with 10 vertices and 11 edges.

6764 is the sum of the first 18 Fibonacci numbers.

6765 is the 20th Fibonacci number.

6768 has a 9th root that starts 2.664444666....

6769 is the Stirling number of the first kind s(8,4).

6772 = 6666 + 7 + 77 + 22.

6779 = 6666 + 7 + 7 + 99.

6780 has the same digits as the 6780th prime.

6786 is a triangular number whose internal digits are triangular and whose external digits are triangular.

6788 is the smallest number with multiplicative persistence 6.

6789 is the largest 4-digit number with increasing digits.

6791 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6792 is a value of n for which n and 2n together use each digit 1-9 exactly once.

6793 is the smallest prime so that it and the next 2 primes all end in 3.

6794 has the property that dropping its first and last digits gives its largest prime factor.

6797 is a number whose sum of divisors is a 5th power.

6801 has a 4th power that is the sum of four 4th powers.

6802 is the number of ways to move a rook from corner to opposite corner on a 6×6 chessboard.

6811 is not the sum of a square, a cube, a 4th power, and a 5th power.

6813 is the smallest number whose 6th power has 24 digits.

6816 is the index of a triangular number containing only 3 different digits.

6818 = 18 + 28 + 38.

6819 = 20457 / 3, and each digit is contained in the equation exactly once.

6820 is the number of regions formed when all diagonals are drawn in a regular 23-gon.

6822 uses the same digits as φ(6822).

6825 is an odd primitive abundant number.

6828 is the number of ways to start with a knight in the corner of an 8×8 chessboard, make 8 moves, and end on the same square.

6831 is a structured truncated octahedral number.

6837 is the number of 8-digit squares.

6839 is a value of n for which n and 8n together use each digit 1-9 exactly once.

6840 is the number of ways to place 2 non-attacking kings on a 11×11 chessboard.

6842 is the number of partitions of 31.

6845 would be prime if preceded and followed by a 1, 3, 7, or 9.

6849 is a value of n for which 2n and 3n together use each digit exactly once.

6850 is the smallest value of n for which n, n+1, n+2, n+3, n+4, and n+5 have the same number of prime factors.

6853 is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors.

6859 = 193.

6860 is a heptagonal pyramidal number.

6861 is a value of n for which σ(n-1) + σ(n+1) = σ(2n).

6863 is a prime that is the sum of the square of a prime and the cube of a prime.

6864 = 6666 + 88 + 66 + 44.

6865 is the maximum value of n so that there exist 5 denominations of stamps so that every postage from 1 to n can be paid for with at most 17 stamps.

6867 can be written as the sum of 2, 3, 4, or 5 positive cubes.

6868 is the larger number in a Ruth-Aaron pair.

6874 is equal to the sum of its anti-divisors.

6875 is 3-automorphic.

6879 is the number of planar partitions of 15.

6880 is a vampire number.

6886 is a palindrome in base 9 and in base 10.

6888 has a square with 3/4 of the digits are the same.

6889 is a strobogrammatic square.

6895 is a value of n for which 2n and 7n together use each digit exactly once.

6896 has a square root whose decimal part starts with the digits 0-9 in some order.

6902 is the number of Hamiltonian paths of a 3×10 rectangle graph.

6903 is a value of n for which σ(n-1) = σ(n+1).

6905 has a 5th root whose decimal part starts with the digits 1-9 in some order.

6912 = 6 × 9 × 1 × 27.

6917 is a value of n for which n! - 1 is prime.

6918 = 20754 / 3, and each digit is contained in the equation exactly once.

6919 is the number of non-invertible knots with 13 crossings.

6922 is the number of polycubes containing 8 cubes.

6924 is the magic constant of a 24×24 magic square.

6927 is a value of n for which n and 2n together use each digit 1-9 exactly once.

6928 is the number of inequivalent binary linear codes of length 11.

6930 is the square root of a triangular number.

6931 has the same digits as the 6931st prime.

6935 is the smallest number whose cube contains six 3's.

6936 is the number of ways to legally add 2 sets of parentheses to a product of 16 variables.

6939 is a value of n for which 3n and 5n together use each digit exactly once.

6940 is the sum of its proper divisors that contain the digit 3.

6941 has a square with the first 3 digits the same as the last 3 digits.

6942 is the number of labeled topologies with 5 elements.

6944 is the number of degree sequences for graphs with 6 vertices.

6949 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with integer dimensions less than 16.

6951 has exactly the same digits in 3 different bases.

6952 = 1738 × 4 and each digit from 1-9 is contained in the equation exactly once.

6953 = 66 + 999 + 5555 + 333.

6954 is the trinomial coefficient T(19,15).

6956 is the number of triangles formed by drawing all diagonals of a regular 12-gon.

6960 is the number of ways to place 2 non-attacking queens on a 10×10 chessboard.

6966 is the number of planar graphs with 8 vertices.

6969 is a strobogrammatic number.

6972 is the number of possible positions in Checkers containing 2 checkers.

6976 is the number of binary 5×5 matrices A with the property that A2=0 (mod 2).

6982 is a value of n for which the sum of the first n composite number numbers is a square.

6983 is the smallest prime that can only be made into 1 other prime by changing a single digit.

6984 can be written as the sum of 2, 3, 4, or 5 positive cubes.

6987 is the number of digits of the 26th Mersenne prime.

6989 has the property that the concatenation of its prime factors in increasing order is a square.

6991 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

6996 is a palindrome n so that n(n+8) is also palindromic.

6998 is a member of the Fibonacci-type sequence starting with 4 and 9.

6999 is the smallest number whose digits add to 33.

7000 has a sum of digits equal to its largest prime factor.

7001 is the number of 13-hexes that tile the plane by translation.

7002 is the number of arrangements of 4 non-attacking queens on a 8×8 chessboard.

7003 is the number of graphs with 9 vertices that have 8 automorphisms.

7014 has a square with the last 3 digits the same as the 3 digits before that.

7015 has a cube root whose decimal part starts with the digits 1-9 in some order.

7019 is a prime that remains prime if any digit is deleted.

7030 is an octagonal pyramidal number.

7032 is the number of ternary square-free words of length 24.

7039 = 28156 / 4, and each digit is contained in the equation exactly once.

7040 has a sum of digits equal to its largest prime factor.

7055 is a Lucas-Carmichael number.

7056 is a square that is the product of two triangular numbers.

7057 is a Cuban prime.

7060 has the property that the sum of the squares of its divisors ends with the digits 7060.

7066 is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 13 stamps.

7068 is the number of series-reduced planted trees with 11 leaves.

7071 is the smallest number whose square contains 4 consecutive 9's.

7072 is the generalized Catalan number C(10,7).

7073 is a Leyland number.

7075 is the number of ways to stack 35 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

7084 is the generalized Catalan number C(19,4).

7089 is a value of n for which cos(n) is smaller than any previous integer.

7092 is the number of possible positions in Othello after 3 moves by both players.

7093 has a 6th root that starts 4.38333833....

7094 is the number of ways to place 34 points on a 17×17 grid so that no 3 points are on a line.

7096 is the number of 8-digit perfect powers.

7098 is the trinomial coefficient T(14,9).

7101 has a 4th power that is the sum of four 4th powers.

7102 is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged.

7106 is an octahedral number.

7108 is the number of partitions of 56 into distinct parts.

7117 is a number whose sum of divisors is a 5th power.

7119 has the same digits as the 7119th prime.

7120 is the number of 2×2 singular matrices mod 10.

7123 is the number of 2-connected graphs with 8 vertices.

7140 is the largest number which is both triangular and tetrahedral.

7142 is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with integer dimensions less than 20.

7143 is 7-automorphic.

7145 has a square with the first 3 digits the same as the next 3 digits.

7150 has a sum of digits equal to its largest prime factor.

7152 has a square with the first 3 digits the same as the next 3 digits.

7159 has a square with the first 3 digits the same as the next 3 digits.

7161 is a Kaprekar constant in base 2.

7164 is a value of n for which n8, n9, n10, and n11 have the same digit sum.

7170 is a value of n for which σ(n-1) = σ(n+1).

7172 is a Kaprekar number for cubes.

7174 is the maximum number of pieces a torus can be cut into with 34 cuts.

7175 is a centered octahedral number.

7176 is the maximum number of regions a cube can be cut into with 35 cuts.

7187 is the smallest number that can not be formed using the digits 0-8 at most once, together with the symbols +, –, × and ÷.

7188 is the number of ways to permute 5 red, 5 white, and 5 blue balls.

7189 is the number of ways to color the vertices of a square with 13 colors, up to rotation.

7192 is a weird number.

7193 is a right-truncatable prime.

7197 is the smallest number whose 7th power has 27 digits.

7200 is the order of a perfect group.

7201 is the number of 2×2 singular matrices mod 19.

7209 has a 4th power that is the sum of four 4th powers.

7212 is the number of unordered ways to write 1 as a sum of reciprocals of integers no larger than 20.

7225 is the number of ways to 17-color the faces of a tetrahedron.

7226 has a cube root that starts 19.3330030330....

7230 is the sum of consecutive squares in 2 ways.

7235 is a value of n for which 4n and 5n together use each digit exactly once.

7236 uses the same digits as φ(7236).

7240 = 1111 in base 19.

7241 is the number of asymmetric trees with 19 vertices.

7245 appears inside its 4th power.

7248 is the number of lines through exactly 2 points of a 14×14 grid of points.

7253 has a square that remains square when a 6 is appended to it.

7254 = 186 × 39 and each digit is contained in the equation exactly once.

7256 is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors.

7260 is a doubly triangular numbers.

7269 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7271 and its reverse are both differences of positive cubes.

7272 is a Kaprekar number.

7281 is a value of n for which 3n and 7n together use each digit exactly once.

7285 has a 7th power that contains the same digits as 54410.

7286 is the number of subsets of {1,2,3,...,16} that have a sum divisible by 9.

7293 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7295 is a value of n for which 4n and 5n together use each digit exactly once.

7297 is a Proth prime.

7306 is the smallest number whose 7th power starts with 7 identical digits.

7311 is the number of symmetric plane partitions of 33.

7312 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7314 is the smallest number so that it and its successor are both products of 4 distinct primes.

7315 = 22C4.

7318 is the number of functions from 10 unlabeled points to themselves.

7320 is the number of triangles of any size contained in the triangle of side 30 on a triangular grid.

7321 is the number of intersections when all the diagonals of a regular 24-gon are drawn.

7322 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole on a side.

7326 = 1 × 22 × 333.

7327 is a number whose sum of divisors is a 5th power.

7329 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7330 is the number of unsymmetrical ways to dissect a regular 14-gon into 12 triangles.

7331 is a right-truncatable prime.

7333 is a right-truncatable prime.

7336 is the number of ways to color the vertices of a triangle with 28 colors, up to rotation.

7337 is a hexagonal pyramidal number.

7338 is the closest integer to 17π.

7339 has a 4th power that is the sum of four 4th powers.

7341 has the same digits as the 7341st prime.

7342 is the number of ways to stack 29 pennies in contiguous rows so that each penny lies on the table or on two pennies.

7344 is a value of n for which 4n and 7n together use each digit exactly once.

7345 has the same digits as the 7345th prime.

7351 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

7353 is the largest number n known so that both n and n3 have only odd digits.

7356 is a value of n for which 5n and 7n together use each digit exactly once.

7358 is a composite number that remains composite when preceded or followed by any digit.

7359 is a Lucas 6-step number.

7360 can be written as the product of a number and its reverse in 2 different ways.

7361 is the number of ways to play the first 5 moves in Checkers.

7364 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7366 is the maximum number of regions space can be divided into by 29 spheres.

7371 has a base 2 representation that begins with its base 9 representation.

7375 is a member of the Fibonacci-type sequence starting with 1 and 4.

7376 is a structured truncated tetrahedral number.

7380 is the number of numbers with 4 or fewer digits that do not contain any 0's.

7381 = 11111 in base 9.

7383 has a 4th power that is 1/2 of the sum of three 4th powers.

7384 has the same digits as the 7384th prime.

7385 is a Keith number.

7387 is the product of two consecutive primes.

7393 is a right-truncatable prime.

7396 has a 4th root whose decimal part starts with the digits 1-9 in some order.

7403 is the smallest number that can not be formed using the digit 1 at most 28 times, together with the symbols +, –, × and ÷.

7404 = 6 + 66 + 666 + 6666.

7410 = 361 + 362 + . . . + 380 = 381 + 382 + . . . + 399.

7413 is the number of even permutations on 8 elements with no fixed points.

7414 is a value of n for which φ(n) = φ(reverse(n)).

7416 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7420 is the number of permutations of 8 items that fix 2 elements.

7421 is a value of n for which 4n and 5n together use each digit exactly once.

7422 is the sum of its proper divisors that contain the digit 7.

7424 and its successor are both abundant.

7425 is an odd primitive abundant number.

7427 is the number of inequivalent asymmetric Ferrers graphs with 35 points.

7429 is the product of 3 consecutive primes.

7430 is the number of labeled commutative monoids of order 5.

7433 is a prime that remains prime if any digit is deleted.

7435 is a cubic star number.

7436 is the number of 6×6 alternating sign matrices.

7444 is a value of n for which cos(n) is smaller than any previous integer.

7447 is a palindrome in base 2 and in base 10.

7448 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

7456 is the number of inequivalent Ferrers graphs with 35 points.

7462 is the number of multigraphs with 26 vertices and 4 edges.

7464 is a structured hexagonal diamond number.

7465 = 54321 in base 6.

7469 is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with integer dimensions less than 21.

7471 is a centered cube number.

7475 has a sum of digits equal to its largest prime factor.

7480 is a value of n for which 2nCn is divisible by n2.

7485 is the number of conjugacy classes of the alternating group A35.

7488 = (12 × 13 × 14 × 15 × 16) / (12 + 13 + 14 + 15 + 16) .

7490 has a square with the last 3 digits the same as the 3 digits before that.

7491 has a base 8 representation which is the reverse of its base 7 representation.

7494 is the sum of its proper divisors that contain the digit 4.

7496 = 777 + 44 + 9 + 6666.

7497 is a hendecagonal pyramidal number.

7499 is the smallest number whose 8th power has 31 digits.

7500 is the order of a perfect group.

7508 would be prime if preceded and followed by a 1, 3, 7, or 9.

7509 has a 6th root whose decimal part starts with the digits 1-9 in some order.

7512 is the sum of its proper divisors that contain the digit 5.

7515 has the property that the sum of its prime factors is equal to the product of its digits.

7519 is a member of the Fibonacci-type sequence starting with 1 and 7.

7524 is the number of rectangles with corners on an 12×12 grid of points.

7525 has a square with the last 3 digits the same as the 3 digits before that.

7528 is the number of ways, up to rotation and reflection, of dissecting a regular 14-gon into 12 triangles.

7531 has digits in arithmetic sequence.

7532 has a square comprised of the digits 0-7.

7541 is an Eisenstein-Mersenne prime.

7542 is a value of n for which 4n and 7n together use each digit exactly once.

7546 is the number of series-reduced planted trees with 19 vertices.

7547 is the maximum number of regions a circle can be cut into by joining 21 points on the circumference with straight lines.

7549 is the largest known prime p where no numbers of the form p-n2 are prime.

7551 is a value of n for which φ(n) + φ(n+1) divides σ(n) + σ(n+1).

7552 is the number of arrangements of 6 non-attacking queens on a 10×6 chessboard.

7557 is a palindrome that is the sum of the first 37 palindromes.

7560 is the smallest number with 64 divisors.

7561 is a Markov number.

7562 would be prime if preceded and followed by a 1, 3, 7, or 9.

7574 is the sum of consecutive squares in 2 ways.

7581 is the number of monotone Boolean functions of 5 variables.

7586 = 777 + 55 + 88 + 6666.

7590 is a number whose sum of divisors is a 4th power.

7595 is the number of simplicial polyhedra with 12 vertices.

7597 is a number whose sum of divisors is a 5th power.

7600 is a substring of any power of itself.

7614 is a value of n for which n and 7n together use each digit 1-9 exactly once.

7615 is a value of n for which σ(n+1) = 2σ(n).

7617 is a hexanacci number.

7618 has a cube that contains only digits 4 and smaller.

7620 is the number of multigraphs with 5 vertices and 14 edges.

7625 is a value of n for which σ(φ(n)) = 2σ(n).

7627 is a value of n for which σ(φ(n)) = 2σ(n).

7629 is a value of n for which n and 5n together use each digit 1-9 exactly once.

7632 is a value of n for which 5n and 6n together use each digit exactly once.

7635 is a centered tetrahedral number.

7639 is the number of rooted ternary trees with 13 vertices.

7647 is a Keith number.

7648 is the number of ways a 10×1 rectangle can be surrounded by 10×1 rectangles.

7650 can be written as the product of a number and its reverse in 2 different ways.

7651 is a value of n for which 2nCn is not divisible by 3, 5, or 7.

7652 is a value of n for which n2 and n3 use the same digits.

7654 has digits in arithmetic sequence.

7658 is the largest number known that does not have any digits in common with its cube.

7659 is the number of planar graphs with 22 vertices, all with degree 5 or more.

7663 is the product of two primes which are reverses of each other.

7664 is the Entringer number E(8,6).

7665 is a Kaprekar constant in base 2.

7667 is a palindrome in base 6 and in base 10.

7669 is the number of integers with complexity 31.

7672 = 777 + 6666 + 7 + 222.

7673 is the smallest number with the property that its first 8 multiples contain the digit 3.

7679 = 7 + 6666 + 7 + 999.

7680 is the number of possible rook moves on a 16×16 chessboard.

7681 is a Proth prime.

7683 is a truncated tetrahedral number.

7685 is the number of necklaces possible with 18 beads, each being one of 2 colors.

7686 is a value of n for which 7n and 9n together use each digit exactly once.

7688 is an Achilles number.

7692 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7693 is a value of n for which the sum of the first n primes is a palindrome.

7695 and its successor are both divisible by 4th powers.

7698 has a square with the first 3 digits the same as the next 3 digits.

7700 is a value of n for which 2φ(n) = φ(n+1).

7703 has a 4th power that is the sum of four 4th powers.

7710 is the number of degree 17 irreducible polynomials over GF(2).

7712 is the number of necklaces (that can't be turned over) possible with 17 beads, each being one of 2 colors.

7713 is a value of n for which 4n and 9n together use each digit exactly once.

7714 is the sum of the first 28 squares.

7721 is the smallest value of n for which 3n contains 8 consecutive 3's.

7724 is the smallest number that can not be written using +, ×, and 5 Fibonacci numbers.

7727 is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged.

7732 and the two numbers before it and after it are all products of exactly 3 primes.

7734 is the sum of its proper divisors that contain the digit 8.

7736 is the number of labeled Eulerian digraphs with 5 vertices.

7738 has the property that dropping its first and last digits gives its largest prime factor.

7739 is a Padovan number.

7741 is the number of trees with 15 vertices.

7743 is the smallest number whose 9th power has 35 digits.

7744 is the smallest known square with no isolated digits.

7745 and its reverse are both one more than a square.

7746 is the number permutations of {1,2,3,...,21} where adjacent numbers differ by no more than 2.

7752 is the generalized Catalan number C(14,5).

7754 is the number of binary cube-free words of length 21.

7755 is the index of a prime Woodall number.

7765 is the number of ways to tile a 7×5 rectangle with integer-sided squares.

7770 = 37C3.

7772 has a square root whose decimal part starts with the digits 1-9 in some order.

7775 = 55555 in base 6.

7776 is a 5th power whose digits are non-increasing.

7777 is a Kaprekar number.

7778 is the closest integer to 27e.

7785 is a value of n for which 5n and 6n together use each digit exactly once.

7788 is the index of a triangular number containing only 3 different digits.

7792 has a square that is the sum of a cube and 5th power.

7793 is the smallest prime so that it and the next 5 primes are all equal to 5 (mod 6).

7795 has the same digits as the 7795th prime.

7799 is a value of n for which cos(n) is smaller than any previous integer.

7800 is the order of a non-cyclic simple group.

7803 is an Achilles number.

7805 is the maximum number of pieces a torus can be cut into with 35 cuts.

7807 is the maximum number of regions a cube can be cut into with 36 cuts.

7808 is the number of 4×4 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner.

7810 has the property that its square is the concatenation of two consecutive numbers.

7811 is the number of ordered sequences of coins totaling 32 cents.

7812 = 222222 in base 5.

7820 is the Stirling number of the second kind S(17,15).

7821 is a value of n for which 2n and 9n together use each digit exactly once.

7824 is a value of n for which 5n and 7n together use each digit exactly once.

7825 is a rhombic dodecahedral number.

7826 is the number of necklaces possible with 6 beads, each being one of 6 colors.

7835 would be prime if preceded and followed by a 1, 3, 7, or 9.

7848 is the number of connected 5-regular graphs with 12 vertices.

7849 is the number of connected 6-regular graphs with 12 vertices.

7851 = 7777 + 8 + 55 + 11.

7852 = 1963 × 4, and each digit from 1-9 is contained in the equation exactly once.

7853 is the largest prime factor of 11! - 1.

7854 is a number whose sum of divisors is a 4th power.

7856 and its successor are both the product of a prime and the 4th power of a prime.

7860 is the number of nonisomorphic 3-state automata with binary inputs and outputs.

7874 is the smallest number n for which n concatenated with n+2 is a square.

7875 is an odd abundant number.

7880 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 26 stamps.

7882 is a structured pentagonal hexacontahedral number.

7884 is a value of n for which 2n and 5n together use each digit exactly once.

7887 is the index of a pentagonal number which is twice another pentagonal number.

7888 is a value of n where φ(n) is the product of the digits of n.

7890 is an icosahedral number.

7894 is a value of n for which n and 8n together use each digit 1-9 exactly once.

7895 is the number of multigraphs with 6 vertices and 11 edges.

7905 is a Kaprekar constant in base 2.

7908 has the same digits as the 7908th prime.

7909 is a Keith number.

7912 is a weird number.

7913 is a value of n for which σ(n-1) = σ(n+1).

7917 is the number of partitions of 57 into distinct parts.

7919 is the 1000th prime.

7920 is the order of the smallest sporadic group.

7921 is the square of a Fibonacci number.

7922 has the property that the sum of its prime factors is equal to the product of its digits.

7923 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7926 is the diameter of the earth in miles.

7928 is a Friedman number.

7931 is a heptagonal pyramidal number.

7932 is a value of n for which n and 2n together use each digit 1-9 exactly once.

7936 is the 5th tangent number.

7937 is the smallest number whose cube contains 5 consecutive 9's.

7939, when followed by any of its digits, is prime.

7941 = 7777 + 9 + 44 + 111.

7942 = 7777 + 99 + 44 + 22.

7946 = 7777 + 99 + 4 + 66.

7953 is the number of domino tilings of a 3×14 rectangle.

7954 is the smallest value of n for which 5n + n is prime.

7956 is a value of n for which n and 4n together use each digit 1-9 exactly once.

7960 is a structured deltoidal hexacontahedral number.

7964 is a value of n for which φ(n) = φ(reverse(n)).

7969 has a square that is formed by 3 squares that overlap by 1 digit.

7980 is the smallest number whose divisors contain every digit at least 7 times.

7983 is a Lucas 8-step number.

7986 = 11 × 22 × 33.

7992 can be written as the difference between two positive cubes in more than one way.

7993 is one less than twice its reverse.

7994 has a 5th power that is closer to a cube than a square.

7997 is a palindrome in base 4 and in base 10.

7999, when followed by any of its digits, is prime.

8000 is the smallest cube which is also the sum of 4 consecutive cubes.

8001 is a Kaprekar constant in base 2.

8002 is the index of a triangular number containing only 3 different digits.

8003 has the property that if each digit is replaced by its square, the resulting number is a square.

8004 has a square with the first 3 digits the same as the next 3 digits.

8008 = 16C6.

8010 uses the same digits as π(8010).

8012 is the number of 3-connected planar maps with 18 edges.

8016 has a square with the last 3 digits the same as the 3 digits before that.

8022 uses the same digits as φ(8022).

8026 is the number of planar partitions of 19.

8042 is the largest number known which cannot be written as a sum of 7 or fewer cubes.

8045 is the number of 6-digit twin primes.

8051 is the number of partitions of 52 in which no part occurs only once.

8056 is the number of triangles of any size contained in the triangle of side 31 on a triangular grid.

8064 = (1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9) / (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9).

8071 is the number of connected graphs with 11 edges.

8074 is the trinomial coefficient T(12,6).

8077 is a value of n for which n2 and n3 use the same digits.

8080 has a square root that has four 8's immediately after the decimal point.

8082 has a square comprised of the digits 1-8.

8083 is a value of n for which n concatenated with n-2 is square.

8085 is an odd primitive abundant number.

8087 is a Lucas 9-step number.

8089 is the pseudosquare modulo 13.

8090 is a Perrin number.

8092 is a Friedman number.

8100 is divisible by its reverse.

8103 is the closest integer to e9.

8104 is equal to the sum of its anti-divisors.

8118 is a strobogrammatic number.

8119 is an NSW number.

8121 is the smallest number whose cube contains seven 5's.

8125 is the smallest number that can be written as the sum of 2 squares in 5 ways.

8128 is the 4th perfect number.

8129 is a member of the Fibonacci-type sequence starting with 2 and 7.

8135 is the 7th central pentanomial coefficient.

8136 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

8149 is a value of n for which 2n and 7n together use each digit exactly once.

8152 is the number of symmetric arrangements of 8 non-attacking queens on a 8×8 chessboard.

8154 is a value of n for which cos(n) is smaller than any previous integer.

8156 has a cube that is only 24 away from a square.

8165 has a square that begins with four 6's.

8169 = 24507 / 3, and each digit is contained in the equation exactly once.

8170 is an enneagonal pyramidal number.

8174 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8176 is a stella octangula number.

8178 is the number of ways 13 people can line up so that only one person has a taller person in front of him.

8179 is a value of n for which 4n and 5n together use each digit exactly once.

8180 is the maximum number of regions space can be divided into by 30 spheres.

8184 has exactly the same digits in 3 different bases.

8189 is the index of a triangular number containing only 3 different digits.

8190 is a harmonic divisor number.

8191 is a Mersenne prime.

8192 is the smallest non-trivial 13th power.

8194 is the number of subsets of the 26th roots of unity that add to 0.

8195 is the number of 17-ominoes with a horizontal or vertical line of symmetry.

8198 is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged.

8200 = 8 + 213 + 0 + 0.

8201 = 8 + 213 + 0 + 1.

8202 = 8 + 213 + 0 + 2.

8203 = 8 + 213 + 0 + 3.

8204 = 8 + 213 + 0 + 4.

8205 = 8 + 213 + 0 + 5.

8206 = 8 + 213 + 0 + 6.

8207 = 8 + 213 + 0 + 7.

8208 is a narcissistic number.

8209 = 8 + 213 + 0 + 9.

8217 is a centered icosahedral number.

8219 is a value of n for which 4n and 5n together use each digit exactly once.

8220 and its reverse are both the averages of twin primes.

8221 has a base 3 representation that begins with its base 6 representation.

8226 is the sum of its proper divisors that contain the digit 4.

8230 is the number of necklaces with 8 beads, each one of 4 colors.

8241 is a value of n for which n has σ(n) / reverse(n) divisors.

8242, when concatenated with one less than it, is square.

8256 is the number of different arrangements (up to rotation and reflection) of 30 non-attacking bishops on a 16×16 chessboard.

8257 is the sum of the squares. of the first 14 primes.

8258 is the number of different positions in Connect Four after 6 moves.

8265 has a 7th root whose decimal part starts with the digits 1-9 in some order.

8368 has a 6th power whose first few digits are 34334444....

8269 is a Cuban prime.

8280 is the smaller number in a Ruth-Aaron pair.

8281 is the only 4-digit square whose two 2-digit pairs are consecutive.

8283 has a base 8 representation which is the reverse of its base 7 representation.

8292 is the number of anisohedral 22-iamonds.

8294 has the property that dropping its first and last digits gives its largest prime factor.

8299 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

8303 = 12345 in base 9.

8304 is the number of subsets of the 18th roots of unity that add to a real number.

8305 has the same digits as the 8305th prime.

8313 is a dodecagonal pyramidal number.

8316 is the sum of 3 consecutive cubes.

8320 is the number of subsets of {1, 1/2, 1/3, ... 1/42} that sum to an integer.

8321 is an Euler pseudoprime.

8338 is a value of n so that n(n+4) is a palindrome.

8340 is a value of n so that (n-1)2 + n2 + (n+1)2 is a palindrome.

8342 is the number of partitions of 53 in which no part occurs only once.

8345 is the smallest number in base 6 to have 6 different digits.

8349 is the number of partitions of 32.

8350 is the trinomial coefficient T(10,1).

8351 has the same digits as the 8351st prime.

8353 is the smallest number whose 4th power contains 5 consecutive 6's.

8355 has the same digits as the 8355th prime.

8361 is a Leyland number.

8363 is the number of 5-digit primes.

8369 is the largest prime factor of 2 × 3 × 5 × 7 × 11 × 13 × 17 - 1.

8372 is a hexagonal pyramidal number.

8373 has a 4th power that is the sum of four 4th powers.

8375 is the smallest number which has equal numbers of every digit in bases 2 and 6.

8378 has a 10th root whose decimal part starts with the digits 1-9 in some order.

8379 is a value of n for which 5n and 8n together use each digit exactly once.

8382 is the index of a triangular number containing only 3 different digits.

8384 is the maximum number of 13th powers needed to sum to any number.

8385 is a structured great rhombicubeoctahedral number.

8388 and its reverse are both the averages of twin primes.

8390 is the number of linear spaces on 7 labeled points.

8392 is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors.

8393 is a value of n for which σ(reverse(n)) = φ(n).

8394 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8396 does not occur in its factorial in base 2.

8397 is the largest known composite number n so that 3nCn = 3n (mod n).

8398 is the 10th super-ballot number.

8400 is the number of legal queen moves in Chess.

8401 has the property that if each digit is replaced by its square, the resulting number is a square.

8403 = 33333 in base 7.

8406 is the number of ways to divide 8 black and 8 white beads into piles.

8408 has 8408 / π(8408) divisors.

8411 would be prime if preceded and followed by a 1, 3, 7, or 9.

8415 is an odd primitive abundant number.

8418 is the number of necklaces possible with 11 beads, each being one of 3 colors.

8419 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8420 is the number of symmetric ways to fold a strip of 20 stamps.

8421 = 1111 in base 20.

8428 is the number of quasi-triominoes that fit inside a 15×15 grid.

8430 and its reverse are both the averages of twin primes.

8433 has a 4th power that is the sum of four 4th powers.

8436 = 38C3.

8439 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8441 is the sum of the cubes of 3 consecutive primes.

8442 is the smallest value of n for which the numbers n-7 through n+7 can not be written as the sum of 2 squares.

8451 is the number of 3×3 matrices in base 3 with determinant 0.

8455 is the trinomial coefficient T(20,16).

8459 is a value of n so that n(n+4) is a palindrome.

8461 is the smallest number whose 9th power starts with 5 identical digits.

8463 is the smaller number in a Ruth-Aaron pair.

8464 is the number of different products of subsets of the set {1, 2, 3, ... 17}.

8467 has a 9th root whose decimal part starts with the digits 1-9 in some order.

8469 is a value of n for which 2n and 3n together use each digit exactly once.

8470 is the number of conjugacy classes in the automorphism group of the 17 dimensional hypercube.

8472 is the maximum number of pieces a torus can be cut into with 36 cuts.

8473 is a centered octahedral number.

8474 is the maximum number of regions a cube can be cut into with 37 cuts.

8475 is the first of four consecutive squareful numbers.

8477 = 10 + 21 + 32 + 43 + 54 + 65.

8481 is an Euler pseudoprime.

8484 is the reciprocal of the sum of the reciprocals of 13332 and its reverse.

8486 = 888 + 44 + 888 + 6666.

8492 is the number of arrangements of 5 non-attacking queens on a 11×5 chessboard.

8493 has a 4th power that is the sum of four 4th powers.

8494 is a value of n for which σ(n) = φ(n) + φ(n-1) + φ(n-2).

8497 is the number of anisohedral 17-hexes.

8499 is the sum of the squares of 3 consecutive primes.

8505 = 21!!!!!!.

8506 is the number of isomers of C13H26 without any double bonds.

8509 is a value of n for which cos(n) is smaller than any previous integer.

8510 is a value of n for which the sum of the first n primes is a palindrome.

8512 is the number of non-intersecting rook paths joining opposite corners of a 5×5 chessboard.

8515 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

8517 has a 4th power that is the sum of four 4th powers.

8521 is a prime that is the average of two 4th powers.

8523 is the first of four consecutive squareful numbers.

8526 is a Rhonda number.

8533 has the property that dropping its first and last digits gives its largest prime factor.

8538 is the sum of its proper divisors that contain the digit 4.

8541 is a value of n so that n(n+6) is a palindrome.

8545 is the number of ways to stack 36 boxes in a line so that each box lies on the table or on a box next to 2 boxes.

8547 is a divisor of 111111.

8548 is the sum of the squares of 4 consecutive primes.

8549 has the property that the sum of its proper divisors is the sum of the squares of its digits.

8555 is the sum of the first 29 squares.

8558 is a Schröder number.

8559 has a square comprised of the digits 1-8.

8562 is the sum of its proper divisors that contain the digit 4.

8563 is the index of a triangular number containing only 3 different digits.

8568 = 18C5.

8569 is a centered dodecahedral number.

8571 shares 3 consecutive digits with one of its prime factors.

8575 is an Achilles number.

8576 can be written as the sum of 2, 3, 4, or 5 positive cubes.

8577 has a 4th power that is the sum of four 4th powers.

8578 appears inside its 4th power.

8579 divides 11 + 22 + 33 + . . . + 85798579.

8580 is the number of subsets of the 28th roots of unity that add to 1.

8582 is the number of monoids of order 7 with 5 idempotents.

8586 has exactly the same digits in 3 different bases.

8586 is a house number.

8599 is the number of forests with 14 vertices.

8602 is the generalized Catalan number C(20,4).

8610 = 400 + 401 + . . . + 420 = 421 + 422 + . . . + 440.

8614 and its prime factors contain every digit from 1-9 exactly once.

8626 is the number of asymmetric trees with 13 vertices.

8627 is a value of n for which 2n and 7n together use each digit exactly once.

8631 is a value of n for which 3n and 7n together use each digit exactly once.

8633 is the product of two consecutive primes.

8637 has a 4th power that is the sum of four 4th powers.

8638 = 7 + 77 + 777 + 7777.

8640 = 2! × 3! × 6!.

8641 is the number of ways to tile a 3×25 rectangle with 3×1 rectangles.

8642 has digits in arithmetic sequence.

8646 divides 28646 + 2.

8649 is a value of n for which 2n and 7n together use each digit exactly once.

8657 is the number of ways to tile a 4×30 rectangle with 4×1 rectangles.

8658 is the sum of the first 4 perfect numbers.

8663 has the property that if each digit is replaced by its square, the resulting number is a square.

8664 = 888 + 6666 + 666 + 444.

8666 has a 9th root whose decimal part starts with the digits 1-9 in some order.

8669 is the maximum value of n so that there exist 5 denominations of stamps so that every postage from 1 to n can be paid for with at most 18 stamps.

8670 is a value of n for which n!! - 1 is prime.

8672 is the number of 14-ominoes that tile the plane by translation.

8680 has a base 5 representation that ends with its base 7 representation.

8681 has a base 5 representation that ends with its base 7 representation.

8682 has a base 5 representation that ends with its base 7 representation.

8683 has a base 5 representation that ends with its base 7 representation.

8684 has a base 5 representation that ends with its base 7 representation.

8688 is the number of possible configurations of pegs (up to symmetry) after 26 jumps in solitaire.

8695 is a centered tetrahedral number.

8697 is a structured octagonal anti-diamond number.

8698 is a strobogrammatic number.

8703 has a cube that is the sum of 3 positive cubes.

8712 is 4 times its reverse.

8714 is the number of ways 24 people around a round table can shake hands in a non-crossing way, up to rotation.

8718 is the smallest n for which Σk≤n 1/(k ln k) ≥ 3.

8721 is a value of n for which φ(n) and σ(n) are square.

8732 has exactly the same digits in 3 different bases.

8736 is the smallest number that appears in its factorial 10 times.

8739 is a member of the Fibonacci-type sequence starting with 3 and 7.

8743 is a number whose sum of divisors is a 4th power.

8744 is the number of subsets of {1,2,3,...,17} that have a sum divisible by 15.

8745 is the number of ways to divide a 13×13 grid of points into two sets using a straight line.

8748 is the largest number whose prime factors add to 25.

8751 is a perfect totient number.

8753 = 88 + 7777 + 555 + 333.

8758 = 88 + 7777 + 5 + 888.

8760 is the number of ways to place 2 non-attacking bishops on a 10×10 chessboard.

8761 is the number of ordered partitions of 25 into distinct parts.

8763 and its successor have the same digits in their prime factorization.

8765 has digits in arithmetic sequence.

8772 is the sum of the first eight 4th powers.

8778 is both a triangular number and 3 times a triangular number.

8779 is is the largest prime factor of 100000000001.

8781 is the closest integer to 18π.

8784 is a value of n for which 2n and 5n together use each digit exactly once.

8785 is the number of 13-iamonds without holes.

8788 is an Achilles number.

8793 is a value of n for which n!!! - 1 is prime.

8796 is a value of n for which 5n and 7n together use each digit exactly once.

8797 is a structured hexagonal diamond number.

8801 is the magic constant of a 26×26 magic square.

8808 is the number of partitions of 58 into distinct parts.

8813 is the number of chiral invertible knots with 14 crossings.

8814 is the number of multigraphs with 27 vertices and 4 edges.

8816 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

8819 is the smallest number whose square begins with four 7's.

8820 is a highly abundant number.

8821 has the property that if each of its digits is replaced by its cube, the result is a square.

8225 are the first 4 digits of 88225.

8826 is the sum of its proper divisors that contain the digit 4.

8829 is a value of n for which 6n and 7n together use each digit exactly once.

8831 would be prime if preceded and followed by a 1, 3, 7, or 9.

8833 = 882 + 332.

8835 is the index of a triangular number containing only 3 different digits.

8837 is the smallest number that can not be written as the sum of 3 volumes of rectangular boxes with integer dimensions less than 17.

8838 and its reverse are both the averages of twin primes.

8840 is the number of triangles of any size contained in the triangle of side 32 on a triangular grid.

8843 is the smallest number that can not be written as the sum of 2 volumes of rectangular boxes with integer dimensions less than 22.

8854 is the number of possible rows in a 20×20 crossword puzzle.

8855 is a Lucas-Carmichael number.

8856 is the number of subsets of {1,2,3,...,16} that have an integer average.

8857 is a structured truncated tetrahedral number.

8860 is the smallest number n so that n+3, n2+32, n4+34, and n8+38 are all prime.

8864 is a value of n for which cos(n) is smaller than any previous integer.

8867 is the smallest prime with multiplicative persistence 6.

8874 has a square that is the concatenation of two consecutive even numbers.

8878 is the number of intersections when all the diagonals of a regular 23-gon are drawn.

8883 does not occur in its factorial in base 2.

8887 is a value of n for which σ(n) is a repdigit.

8888 is a repdigit.

8892 is a betrothed number.

8902 is the number of possibilities for the first 1.5 moves in Chess.

8905 multiplied by its successor gives a number concatenated with itself.

8910 is divisible by its reverse.

8911 is a Carmichael number.

8913 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 27 stamps.

8922 is the sum of its proper divisors that contain the digit 4.

8923 is the numerator of 1 / 11 + 1 / 22 + 1 / 33 + 1 / 44.

8925 is an odd primitive abundant number.

8930 = 8888 + 9 + 33 + 0.

8931 = 8888 + 9 + 33 + 1.

8932 = 8888 + 9 + 33 + 2.

8933 = 8888 + 9 + 33 + 3.

8934 = 8888 + 9 + 33 + 4.

8935 = 8888 + 9 + 33 + 5.

8936 = 8888 + 9 + 33 + 6.

8937 = 8888 + 9 + 33 + 7.

8938 = 8888 + 9 + 33 + 8.

8939 = 8888 + 9 + 33 + 9.

8942 is a value of n for which n and 8n together use each digit 1-9 exactly once.

8944 is the sum of the cubes of the first 7 primes.

8950 has a 4th root whose decimal part starts with the digits 1-9 in some order.

8953 is the 10th central trinomial coefficient.

8954 is the first of four consecutive squareful numbers.

8958 has a 4th power whose product of digits is also a 4th power.

8964 is the smallest number with the property that its first 6 multiples contain the digit 8.

8965 is a value of n for which n2 and n3 use the same digits.

8968 is a strobogrammatic number.

8970 = 8 + 94 + 74 + 0.

8971 = 8 + 94 + 74 + 1.

8972 = 8 + 94 + 74 + 2.

8973 = 8 + 94 + 74 + 3.

8974 = 8 + 94 + 74 + 4.

8975 = 8 + 94 + 74 + 5.

8976 = 8 + 94 + 74 + 6.

8977 = 8 + 94 + 74 + 7.

8978 = 8 + 94 + 74 + 8.

8979 = 8 + 94 + 74 + 9.

8980 is a value of n for which the first n binary digits of π form a prime.

8982 uses the same digits as φ(8982).

8989 is a Delannoy number.

8991 is the smallest number so that it and its successor are both the product of a prime and the 5th power of a prime.

8993 is a Huay rhombic dodecahedral number.

8999 is the smallest number whose digits add to 35.

9000 is the index of a triangular number containing only 3 different digits.

9002 is a value of n so that n(n+7) is a palindrome.

9005 is the number of inequivalent Ferrers graphs with 36 points.

9006 is a strobogrammatic number.

9009 is a centered cube number.

9011 has a square that is the concatenation of two consecutive odd numbers.

9012 is the sum of its proper divisors that contain the digit 5.

9016 is the number of perfect squared rectangles of order 16.

9018 has a square with the last 3 digits the same as the 3 digits before that.

9020 is the number of ways to color the vertices of a triangle with 30 colors, up to rotation.

9023 has the property that the concatenation of its prime factors in increasing order is a square.

9024 is the number of regions formed when all diagonals are drawn in a regular 24-gon.

9025 is a Friedman number.

9028 is the number of ways to tile a 9×4 rectangle with integer-sided squares.

9032 would be prime if preceded and followed by a 1, 3, 7, or 9.

9036 has a 9th power that contains the same digits as 358510.

9037 is a value of n for which 2n and 7n together use each digit exactly once.

9038 is the number of conjugacy classes of the alternating group A36.

9042 is the trinomial coefficient T(11,4).

9045 is the number of ways to 18-color the faces of a tetrahedron.

9048 is the number of regions the complex plane is cut into by drawing lines between all pairs of 24th roots of unity.

9049 is an Eisenstein-Mersenne prime.

9052 is the maximum number of regions space can be divided into by 31 spheres.

9055 is the index of a triangular number containing only 3 different digits.

9056 is a cubic star number.

9059 has an 8th root that starts 3.12345....

9070 has a 4th root whose decimal part starts with the digits 1-9 in some order.

9072 has a base 2 and base 3 representation that end with its base 6 representation.

9073 has a base 2 and base 3 representation that end with its base 6 representation.

9074 has a base 3 representation that ends with its base 6 representation.

9077 is a Markov number.

9078 has a cube whose digits occur with the same frequency.

9079 has a square that is the concatenation of two consecutive decreasing numbers.

9086 is the number of regions formed when all diagonals are drawn in a regular 23-gon.

9091 is the only prime known whose reciprocal has period 10.

9093 has a square with the first 3 digits the same as the next 3 digits.

9099 is the number of ways to 3-color the faces of a dodecahedron.

9101 has a square where the first 6 digits alternate.

9104 has a square with the first 3 digits the same as the next 3 digits.

9105 is the number of possible positions in Checkers after 6 moves.

9108 is a heptagonal pyramidal number.

9109 is the number of regions the complex plane is cut into by drawing lines between all pairs of 23rd roots of unity.

9113 is a narcissistic number in base 5.

9115 has a base 3 representation that begins with its base 6 representation.

9116 is a strobogrammatic number.

9117 is a value of n for which 6n and 7n together use each digit exactly once.

9119 is the number of symmetric plane partitions of 34.

9121 is the number of possibilities for the last 5 digits of a square.

9126 is a pentagonal pyramidal number.

9134 has a 10th root whose decimal part starts with the digits 1-9 in some order.

9135 is a value of n for which 2n and 7n together use each digit exactly once.

9137 has a 4th power that is the sum of four 4th powers.

9139 = 39C3.

9152 and its successor are both divisible by 4th powers.

9153 is a value of n for which 2n and 3n together use each digit exactly once.

9154 is a value of n for which φ(n) and σ(n) are square.

9156 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9158 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9162 is a value of n for which 5n and 8n together use each digit exactly once.

9168 = 27504 / 3, and each digit is contained in the equation exactly once.

9172 is the number of connected planar maps with 7 edges.

9174 is the sum of its proper divisors that contain the digit 5.

9176 is the maximum number of pieces a torus can be cut into with 37 cuts.

9178 is the maximum number of regions a cube can be cut into with 38 cuts.

9179 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

9182 is a value of n for which 4n and 5n together use each digit exactly once.

9183 is the number of sets of distinct positive integers with mean 8.

9185 is a value of n for which 2n and 7n together use each digit exactly once.

9189 is the number of sided 10-ominoes.

9191 is not the sum of a square, a cube, a 4th power, and a 5th power.

9196 has the property that dropping its first and last digits gives its largest prime factor.

9198 is the number of ternary square-free words of length 25.

9201 is a truncated octahedral number.

9214 is the number of ways to stack 30 pennies in contiguous rows so that each penny lies on the table or on two pennies.

9216 is a Friedman number.

9217 is the total number of digits of all binary numbers of length 1-10.

9219 is a value of n for which cos(n) is smaller than any previous integer.

9224 is an octahedral number.

9233 is the number of different arrangements (up to rotation and reflection) of 13 non-attacking queens on a 13×13 chessboard.

9234 is the number of multigraphs with 7 vertices and 10 edges.

9235 is the number of 13-iamonds.

9237 is a value of n for which n and 5n together use each digit 1-9 exactly once.

9240 = 22P3.

9241 is a Cuban prime.

9243 has a 4th power that is the sum of four 4th powers.

9248 is the number of possible rook moves on a 17×17 chessboard.

9250 = (103 + 104 + 105 + 106) / (3 × 4 × 5 × 6).

9252 is the number of necklaces with 10 white and 10 black beads.

9253 is the smallest number that appears in its factorial 9 times.

9261 is a Friedman number.

9267 is a value of n for which n and 2n together use each digit 1-9 exactly once.

9268 is a value of n for which 2φ(n) = φ(n+1).

9272 is a weird number.

9273 is a value of n for which n and 2n together use each digit 1-9 exactly once.

9282 is the product of three consecutive Fibonacci numbers.

9285 is the number of 16-hexes with reflectional symmetry.

9286 is a narcissistic number in base 7.

9287 is the number of stretched 10-ominoes.

9288 can be written as the sum of 2, 3, 4, or 5 positive cubes.

9289 is a tetranacci number.

9298 has the property that the concatenation of its prime factors in increasing order is a square.

9304 = 65128 / 7, and each digit is contained in the equation exactly once.

9305 has the property that if each digit is replaced by its square, the resulting number is a square.

9306 is a value of n for which 3n and 5n together use each digit exactly once.

9310 is a decagonal pyramidal number.

9311 is the index of a prime Fibonacci number.

9313, when followed by any of its digits, is prime.

9315 is a value of n for which 2n and 3n together use each digit exactly once.

9316 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9321 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9324 is the reciprocal of the sum of the reciprocals of 14652 and its reverse.

9327 is a value of n for which n and 2n together use each digit 1-9 exactly once.

9330 is the Stirling number of the second kind S(10,3).

9331 has the property that the sum of its prime factors is equal to the product of its digits.

9339 is a value of n for which φ(n) = φ(n-2) - φ(n-1).

9347 is a value of n for which the sum of square-free divisors of n and n+1 are the same.

9348 has a 8th power that contains the same digits as 35889.

9349 is the 19th Lucas number.

9350 appears inside its 4th power.

9352 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9360 is a value of n for which σ(n-1) = σ(n+1).

9362 = 22222 in base 8.

9363 is the number of tilted rectangles with vertices in a 15×15 grid.

9364 is the number of connected digraphs with 5 vertices.

9367 is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors.

9371 is a prime that remains prime when preceded and followed by one, two, three, or four 3's.

9374 is a value of n for which φ(σ(n)) = φ(n).

9375 has a cube that ends with those digits.

9376 is an automorphic number.

9377 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

9378 is a value of n for which 4n and 5n together use each digit exactly once.

9380 is the number of lines through exactly 2 points of a 15×15 grid of points.

9382 is a value of n for which 4n and 5n together use each digit exactly once.

9383 is the index of a Fibonacci number whose first 9 digits are the digits 1-9 rearranged.

9385 is the sum of consecutive squares in 2 ways.

9386 = 99 + 333 + 8888 + 66.

9391 has a square with the first 3 digits the same as the last 3 digits.

9393 is the number of non-isomorphic 3×3×3 Rubik's cube positions that require exactly 5 quarter turns to solve.

9394 is a value of n so that n(n+8) is a palindrome.

9396 is the number of symmetric 3×3 matrices in base 6 with determinant 0.

9403 = 65821 / 7, and each digit is contained in the equation exactly once.

9406 is the index of a triangular number containing only 3 different digits.

9407 has a 7th root whose decimal part starts with the digits 1-9 in some order.

9408 is the number of reduced 6×6 Latin squares.

9413 has a cube whose digits occur with the same frequency.

9416 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9421 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9424 has the property that the fractional part of π9424 begins .9424....

9426 is a value of n for which 5n and 7n together use each digit exactly once.

9427 is the smallest number that can not be formed using the digit 1 at most 29 times, together with the symbols +, –, × and ÷.

9428 is the smallest number whose square begins with four 8's.

9431 is a number n for which n, n+2, n+6, and n+8 are all prime.

9432 is the number of 3-colored rooted trees with 6 vertices.

9436 is the smallest number whose 15th power contains exactly the same digits as another 15th power.

9439 is prime, and 5 closest primes are all smaller.

9444 has a square with the first 3 digits the same as the next 3 digits.

9445 is the closest integer to 29e.

9450 is the denominator of ζ(8) / π8.

9451 is the number of binary rooted trees with 19 vertices.

9452 is the smallest number whose cube contains 5 consecutive 4's.

9455 is the sum of the first 30 squares.

9465 is an hexagonal prism number.

9468 is the sum of its proper divisors that contain the digit 7.

9471 is an octagonal pyramidal number.

9473 is a Proth prime.

9474 is a narcissistic number.

9477 is the maximum determinant of a binary 13×13 matrix.

9481 is a number whose sum of divisors is a 4th power.

9489 is the closest integer to π8.

9493 is a member of the Fibonacci-type sequence starting with 1 and 9.

9496 is the number of 10×10 symmetric permutation matrices.

9499 has a 5th power whose first few digits are 77337377....

9500 is a hexagonal pyramidal number.

9504 is a betrothed number.

9513 is the smallest number without increasing digits that is divisible by the number formed by writing its digits in increasing order.

9519 has a 4th power that is the sum of four 4th powers.

9520 is an enneagonal pyramidal number.

9523 is a value of n for which 4n and 5n together use each digit exactly once.

9529 is the number of 3×3 sliding puzzle positions that require exactly 18 moves to solve starting with the hole in a corner.

9531 is the index of a prime Woodall number.

9538 is a value of n for which 4n and 5n together use each digit exactly once.

9541 is a value of n for which n and 8n together use each digit 1-9 exactly once.

9542 is the number of ways to place a non-attacking white and black pawn on a 11×11 chessboard.

9551 has the same digits as the 9551st prime.

9552 and the following 34 numbers are composite.

9555 is an odd primitive abundant number.

9563 = 9 + 5555 + 666 + 3333.

9564 is the number of paraffins with 10 carbon atoms.

9568 = 9 + 5 + 666 + 8888.

9574 is a value of n for which cos(n) is smaller than any previous integer.

9576 = 19!!!!!.

9592 is the number of primes with 5 or fewer digits.

9596 is the index of a triangular number containing only 3 different digits.

9601 is a Proth prime.

9602 has the property that if each digit is replaced by its square, the resulting number is a square.

9605, when concatenated with 4 less than itself, is square.

9608 is the number of digraphs with 5 vertices.

9615 is the smallest number whose cube starts with 5 identical digits.

9616 is an icosahedral number.

9623 is the number of symmetric 10-cubes.

9625 has a square formed by inserting a block of digits inside itself.

9627 is a value of n for which n and 5n together use each digit 1-9 exactly once.

9629 is a value of n for which 2n and 7n together use each digit exactly once.

9632 is the number of different arrangements of 4 non-attacking queens on a 4×14 chessboard.

9639 has a 4th power that is the sum of four 4th powers.

9643 is the smallest number that can not be formed using the numbers 20, 21, ... , 27, together with the symbols +, –, × and ÷.

9648 is a factor of the sum of the digits of 96489648.

9653 = 99 + 666 + 5555 + 3333.

9658 = 99 + 666 + 5 + 8888.

9660 is a truncated tetrahedral number.

9670 is the number of 8-digit triangular numbers.

9673 is the number of triangles of any size contained in the triangle of side 33 on a triangular grid.

9677 is a prime that remains prime if any digit is deleted.

9682 is a value of n for which n!! - 1 is prime.

9689 is the exponent of a Mersenne prime.

9691 has the property that the concatenation of its prime factors in increasing order is a square.

9695 is the sum of the digits of 555.

9696 is a strobogrammatic number.

9700 is the number of inequivalent 4-digit strings, where two strings are equivalent if turning one upside down gives the other.

9707 does not occur in its factorial in base 2.

9709 has a cube whose digits occur with the same frequency.

9711 uses the same digits as π(9711).

9716 is the number of Pyramorphix puzzle positions that require exactly 5 moves to solve.

9720 is the order of a perfect group.

9721 is the largest prime factor of 1234567.

9723 is a value of n for which n and 5n together use each digit 1-9 exactly once.

9724 = 1111 in base 21.

9726 is the smallest number in base 5 whose square contains the same digits in the same proportion.

9728 can be written as the sum of 2, 3, 4, or 5 positive cubes.

9738 is the number of trees on 22 vertices with diameter 5.

9747 is an Achilles number.

9748 is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 14 stamps.

9751 is the number of possible configurations of pegs (up to symmetry) after 8 jumps in solitaire.

9753 is a value of n for which 4n and 5n together use each digit exactly once.

9754 is the number of paths between opposite corners of a 3×5 rectangle graph.

9760 can be written as the product of a number and its reverse in 2 different ways.

9764 would be prime if preceded and followed by a 1, 3, 7, or 9.

9765 is an odd primitive abundant number.

9767 is the largest 4 digit prime composed of concatenating two 2 digit primes.

9768 = 2 × 22 × 222.

9770 is the number of Hamiltonian cycles of a 4×12 rectangle graph.

9775 is a number n so that the sum of the digits of nn-1 is divisible by n.

9777 is the number of graphs on 8 vertices with no isolated vertices.

9779 has a square root that has four 8's immediately after the decimal point.

9784 is the number of 2 state Turing machines which halt.

9789 is the smallest number that appears in its factorial 11 times.

9790 is the number of ways to place 2 non-attacking kings on a 12×12 chessboard.

9792 is the number of partitions of 59 into distinct parts.

9793 is the smallest number that can be written as the sum of 4 distinct positive cubes in 5 ways.

9796 has the property that dropping its first and last digits gives its largest prime factor.

9797 is the product of two consecutive primes.

9798 is a number whose sum of divisors is a 4th power.

9799 is a number whose sum of squares of the divisors is a square.

9800 is the largest 4-digit number with single digit prime factors.

9801 is 9 times its reverse.

9802, when concatenated with one less than it, is square.

9805 is the number of subsequences of {1,2,3,...15} in which every odd number has an even neighbor.

9809 is a stella octangula number.

9828 is the order of a non-cyclic simple group.

9831 has a base 6 representation which is the reverse of its base 5 representation.

9839 would be prime if preceded and followed by a 1, 3, 7, or 9.

9841 = 111111111 in base 3.

9843 is the number of vertices in a Sierpinski triangle of order 8.

9849 is a centered tetrahedral number.

9854 is the index of a triangular number containing only 3 different digits.

9855 is a rhombic dodecahedral number.

9857 is a Proth prime.

9858 is a number whose sum of divisors is a 4th power.

9861 is a dodecagonal pyramidal number.

9862 is the number of knight's tours on a 6×6 chessboard.

9865 is the number of digits in the 15th Fermat number.

9868 is the number of hydrocarbons with 10 carbon atoms.

9871 is the largest 4-digit prime with different digits.

9872 = 8 + 88 + 888 + 8888.

9876 is the largest 4-digit number with different digits.

9877 has a 4th power that is the sum of four 4th powers.

9878 has a 10th power whose first few digits are 88448448....

9880 = 40C3.

9886 is a strobogrammatic number.

9888 is the number of connected graphs with 8 vertices whose complements are also connected.

9894 is the number of 3-colored trees with 7 vertices.

9896 is the number of Pyraminx puzzle positions that require exactly 6 moves to solve.

9900 = 100110101011002 = 990010 = 188119 = 119921, each using two digits the same number of times.

9901 is the only prime known whose reciprocal has period 12.

9910 is the number of fixed 9-ominoes.

9911 has the property that the sum of its prime factors is equal to the product of its digits.

9912 is the number of graceful permutations of length 14.

9913, when followed by any of its digits, is prime.

9918 is the maximum number of pieces a torus can be cut into with 38 cuts.

9919 can be written as the difference between two positive cubes in more than one way.

9920 is the maximum number of regions a cube can be cut into with 39 cuts.

9928 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

9929 is the number of 3×3 sliding puzzle positions that require exactly 26 moves to solve starting with the hole on a side.

9933 = 441 + 442 + . . . + 462 = 463 + 464 + . . . + 483.

9941 is the exponent of a Mersenne prime.

9944 = 100110110110002 = 994410 = 2E2E15 = 11BB21, each using two digits the same number of times.

9945 = 17!!!!.

9951 is the number of ways to color the vertices of a triangle with 31 colors, up to rotation.

9959 is a member of the Fibonacci-type sequence starting with 2 and 5.

9960 is the number of 3×3×3 sliding puzzle positions that require exactly 8 moves to solve.

9966 is the largest 4-digit strobogrammatic number.

9973 is the largest 4-digit prime.

9976 has a square formed by inserting a block of digits inside itself.

9984 is the maximum number of regions space can be divided into by 32 spheres.

9985 is the number of hyperbolic knots with 13 crossings.

9988 is the number of prime knots with 13 crossings.

9992 is the number of 2×2×2 Rubik's cube positions that require exactly 5 moves to solve.

9995 has a square formed by inserting a block of digits inside itself.

9996 has a square formed by inserting a block of digits inside itself.

9998 is the smallest number n for which the concatenation of n, (n+1), ... (n+21) is prime.

9999 is a Kaprekar number.

Oh My God.....I am dropped dead......