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400 (number)

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This article is about the numbers 400 to 499. For the year 400 AD, see 400. For other uses, see 400 (disambiguation).
← 399 400 401 →
Cardinalfour hundred
Ordinal400th
(four hundredth)
Factorization24 × 52
Divisors1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
Greek numeralΥ´
Roman numeralCD, cd
Binary1100100002
Ternary1122113
Senary15046
Octal6208
Duodecimal29412
Hexadecimal19016
Hebrewת
ArmenianՆ
Babylonian cuneiform𒐚𒐏
Egyptian hieroglyph𓍥

400 (four hundred) is the natural number following 399 and preceding 401.

Mathematical properties

[edit]

A circle is divided into 400 grads.

Integers from 401 to 499

[edit]

400s

[edit]

401

[edit]

401 is a prime number, a Chen prime,[1] a prime index prime, an Eisenstein prime with no imaginary part, a tetranacci number,[2] a zero of Mertens function,[3] and a member of the Mian–Chowla sequence.[4]

It is the sum of seven consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71) and the sum of nine consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).

402

[edit]

402 = 2 × 3 × 67. It is a sphenic number, a nontotient and a Harshad number. There are 402 graphs with 8 nodes and 9 edges.[5]

403

[edit]

403 = 13 × 31. It is a heptagonal number, a zero of Mertens function,[3] and the smallest number that is the product of an emirp pair.[6]

404

[edit]

404 = 22 × 101, a zero of Mertens function,[3] a nontotient and a noncototient. There are 404 integer partitions of 20 with an alternating permutation.[7]

The HTTP 404 status code is usually sent from a web page if a user attempts to reach a broken or dead link. It has since become one of the most commonly reached, and thus most recognizable errors on the World Wide Web.[8]

405

[edit]

405 = 34 × 5. It is a zero of Mertens function,[3] a Harshad number and a pentagonal pyramidal number.

406

[edit]

406 = 2 × 7 × 29. It is a sphenic number, the 28th triangular number,[9] a centered nonagonal number,[10] an even nontotient, and a Narayana's cow number.[11]

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English Wikisource has original text related to this article:

406 is a poem by John Boyle O'Reilly. It was believed to have been the number of one of O'Reilly's prison cells, and was the number of his first hotel room after he arrived in the United States. Hence the number had a mystical significance to him, as intimated in the poem.

407

[edit]

407 = 11 × 37. It is a zero of Mertens function,[3] a Harshad number, and a Lazy caterer number.[12]It is the sum of the cubes of 4, 0 and 7 (43 + 03 + 73 = 407) and thus a narcissistic number.[13] It is the sum of three consecutive primes (131 + 137 + 139).

408

[edit]

408 = 23 × 3 × 17. It is a Pell number,[14] a zero of Mertens function,[3] an Octagonal number,[15] an Untouchable number[16] and a Harshad number. It is the sum of four consecutive primes (97 + 101 + 103 + 107) and the sum of eight consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).

409

[edit]

409 is a prime number, a Chen prime,[1] and a centered triangular number.[17]

410s

[edit]

410

[edit]

410 = 2 × 5 × 41. It is a sphenic number, a nontotient, a Harshad number, and the sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79). There are 410 triangle-free graphs on 8 vertices.[18]

411

[edit]

411 = 3 × 137. It is a self number.[19]

412

[edit]

412 = 22 × 103. It is a nontotient, a noncototient, and the sum of twelve consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).

41264 + 1 is prime

413

[edit]

413 = 7 × 59. It is a zero of Mertens function,[3] a self number,[19] and a Blum integer.

414

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414 = 2 × 32 × 23. It is a zero of Mertens function,[3] a nontotient, and a Harshad number. There are 414 balanced partitions of 31.[20]

is prime[21]

415

[edit]

415 = 5 × 83. It is a logarithmic number.[22]

416

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416 = 25 × 13. There are independent vertex sets and vertex covers in the 6-sunlet graph[23]

417

[edit]

417 = 3 × 139. It is a Blum integer.

418

[edit]

418 = 2 × 11 × 19. It is a sphenic number,[24] a balanced number.[25] and the fourth 71-gonal number.[26]

It is the sum of the integers between 13 and 31, inclusive.

The sum of the 84 digits of the 22nd unique prime in decimal (having a very distinct set of digits than all other known terms in the sequence).[27]

419

[edit]

419 is a prime number, a Sophie Germain prime,[28] a Chen prime,[1] an Eisenstein prime with no imaginary part, a highly cototient number,[29] and a zero of Mertens function.[3]

420s

[edit]

420

[edit]
Main article: 420 (number)
See also: 420 (cannabis culture)

421

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421 is a prime number, a centered square number,[30] and the sum of five consecutive primes (73 + 79 + 83 + 89 + 97).

422

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422 = 2 × 211. It is a zero of Mertens function[3] and a nontotient. Since 422 = 202 + 20 + 2, 422 is the maximum number of regions into which 21 intersecting circles divide the plane.[31]

423

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423 = 32 × 47. It is a zero of Mertens function[3] and a Harshad number.

There are 423 secondary structures of RNA molecules with 10 nucleotides[32]

424

[edit]

424 = 23 × 53. It is a zero of Mertens function,[3] a refactorable number,[33] a self number[19] and the sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).

425

[edit]

425 = 52 × 17. It is a pentagonal number,[34] a centered tetrahedral number, a zero of Mertens function,[3] and the sum of three consecutive primes (137 + 139 + 149). It is the second number that can be expressed as the sum of two squares in three different ways (425 = 202 + 52 = 192 + 82 = 162 + 132).

426

[edit]

426 = 2 × 3 × 71. It is a sphenic number, a nontotient, and an untouchable number.

427

[edit]

427 = 7 × 61. It is a zero of Mertens function.[3]

427! + 1 is prime.

428

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428 = 22 × 107. It is a zero of Mertens function and a nontotient.

42832 + 1 is prime[35]

429

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429 = 3 × 11 × 13. It is a sphenic number and a Catalan number.[36]

430s

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430

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430 = 2 × 5 × 43. It is a sphenic number and an untouchable number.[16]

431

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431 is a prime number, a Sophie Germain prime,[28] a Chen prime,[1] a prime index prime, an Eisenstein prime with no imaginary part, the fourth Leyland prime of the second kind and the sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73).

432

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432 = 24 × 33 = 42 × 33. It is a Harshad number, a highly totient number,[37] an Achilles number and the sum of the totient function for first 37 integers. It is the sum of four consecutive primes (103 + 107 + 109 + 113). 432! is the first factorial that is not a Harshad number in base 10. An equilateral triangle whose area and perimeter are equal has an area (and perimeter) equal to .

433

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433 is a prime number, a Markov number,[38] and a star number.[39]

434

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434 = 2 × 7 × 31. It is a sphenic number, a nontotient and the sum of six consecutive primes (61 + 67 + 71 + 73 + 79 + 83). It is the maximal number of pieces that can be obtained by cutting an annulus with 28 cuts.[40]

435

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435 = 3 × 5 × 29. It is a sphenic number, a hexagonal number,[41] a self number,[19] and the 29th triangular number.[42] There are 435 compositions of 16 into distinct parts.[43]

436

[edit]

436 = 22 × 109. It is a nontotient, a noncototient, and a lazy caterer number.[12]

437

[edit]

437 = 19 × 23. It is a Blum integer.

438

[edit]

438 = 2 × 3 × 73. It is a sphenic number and a Smith number.[44]

439

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439 is a prime number and a strictly non-palindromic number.[45] It is the sum of three consecutive primes (139 + 149 + 151) and the sum of nine consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).

440s

[edit]

440

[edit]
Main article: 440 (number)

441

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441 = 32 × 72 = 21. It is a centered octagonal number,[46] a refactorable number,[33] and a Harshad number.

441 is also the sum of the cubes of the first 6 natural numbers: 441 = 13 + 23 + 33 + 43 + 53 + 63.

442

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442 = 2 × 13 × 17. It is a sphenic number and the sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).

443

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443 is a prime number, a Sophie Germain prime,[28] a Chen prime,[1] and an Eisenstein prime with no imaginary part.

Mertens function of 443 is -9, a new low which stands until 659.

444

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444 = 22 × 3 × 37. It is a refactorable number,[33] a Harshad number, and a repdigit. There are 444noniamonds without holes.[47]

445

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445 = 5 × 89. There are 445 series-reduced trees with 17 nodes.[48]

446

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446 = 2 × 223. It is a nontotient and a self number.[19]

447

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447 = 3 × 149. There are 447 1's in all partitions of 22 into odd parts.[49]

448

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448 = 26 × 7. It is an untouchable number,[16] a refactorable number,[33] and a Harshad number.

449

[edit]

449 is a prime number, a Chen prime,[1] a Proth prime,[50] an Eisenstein prime with no imaginary part, and the sum of five consecutive primes (79 + 83 + 89 + 97 + 101).

449! is the largest factorial less than 101000.

450s

[edit]

450

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450 = 2 × 32 × 52. It is a nontotient, a refactorable number,[33] a Harshad number, and the sum of totient function for the first 38 integers.

451

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451 = 11 × 41. It is a Wedderburn–Etherington number[51] and a centered decagonal number.[52] It is the smallest number whose reciprocal has period 10.

452

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452 = 22 × 113. There are 452 surface-points of a tetrahedron with edge-length 15.[53]

453

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453 = 3 × 151. It is a Blum integer.

454

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454 = 2 × 227. It is a nontotient and a Smith number.[44]

455

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455 = 5 × 7 × 13. It is a sphenic number and a tetrahedral number.[54]

The sum of the squares of the first 455 primes is divisible by 455.[55]

456

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456 = 23 × 3 × 19. It is a centered pentagonal number,[56] an icosahedral number, the sum of a pair of twin primes (227 + 229), and the sum of four consecutive primes (107 + 109 + 113 + 127).

It is one of the two values of the magical formula, IPSOS, the other being 696.[57]

457

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457 is a prime number, a self number,[19] and the sum of three consecutive primes (149 + 151 + 157).

458

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458 = 2 × 229. It is a nontotient. There are 458partitions of 24 into divisors of 24.[58]

459

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459 = 33 × 17. It is a triangular matchstick number.[59]

460s

[edit]

460

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460 = 22 × 5 × 23. It is a centered triangular number,[17] a dodecagonal number,[60] a Harshad number, and the sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61).

461

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461 is a prime number, a Chen prime,[1] a sexy prime with 467, an Eisenstein prime with no imaginary part, and a prime index prime.

462

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462 = 2 × 3 × 7 × 11. Itis a pronic number,[61] a sparsely totient number,[62] an idoneal number, a stirling number of the second kind , the binomial coefficient , and the sum of six consecutive primes (67 + 71 + 73 + 79 + 83 + 89).

463

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463 is a prime number, a centered heptagonal number,[63] sum of seven consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79). It is the first of seven consecutive primes that are one less than a multiple of 4 (from 463 to 503).

It is a common baseball double play (see baseball positions).

There are 463 days in the synodic period of Ceres.

464

[edit]
See also: 4-6-4

464 = 24 × 29. It is a primitive abundant number.[64] and the maximal number of pieces that can be obtained by cutting an annulus with 29 cuts.[40] Since 464 = 212 + 21 + 2, it is the maximum number of regions into which 22 intersecting circles divide the plane.[31]

465

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465 = 3 × 5 × 31. It is a sphenic number, a member of the Padovan sequence,[65] a Harshad number, and the 30th triangular number.[66]

466

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466 = 2 × 233. It is a noncototient and a lazy caterer number.[12]

467

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467 is a prime number, a safe prime,[67] a sexy prime with 461, a Chen prime,[1] and an Eisenstein prime with no imaginary part.

is prime[21]

468

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468 = 22 × 32 × 13. It is a refactorable number,[33] a self number,[19] a Harshad number and the sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).

469

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469 = 7 × 67. It is a centered hexagonal number.[68]

469! - 1 is prime.

470s

[edit]

470

[edit]

470 = 2 × 5 × 47. It is a sphenic number, a nontotient, a noncototient, and a cake number.

471

[edit]

471 = 3 × 157.It is the sum of three consecutive primes (151 + 157 + 163).

It is a perfect totient number,[69] additionally, φ(471) = φ(σ(471)).[70]

472

[edit]

472 = 23 × 59. It is a nontotient, an untouchable number,[16] and a refactorable number.[33] There are 472 distinct ways to cut a 5 × 5 square into squares with integer sides.[71]

473

[edit]

473 = 11 × 43. It is a Blum integer and the sum of five consecutive primes (83 + 89 + 97 + 101 + 103).

474

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474 = 2 × 3 × 79. It is a sphenic number, a nontotient, a noncototient, an untouchable number,[16] a nonagonal number,[72] the sum of the totient function for first 39 integers, and the sum of eight consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).

475

[edit]

475 = 52 × 19. It is a 49-gonal number and a member of the Mian–Chowla sequence.[4]

476

[edit]

476 = 22 × 7 × 17. It is a Harshad number and an admirable number.[73]

477

[edit]

477 = 32 × 53. It is a pentagonal number.[34]

478

[edit]

478 = 2 × 239. It is a Companion Pell number. There are 478 partitions of 26 that do not contain 1 as a part.[74]

479

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479 is a prime number, a safe prime,[67] a Chen prime,[1] an Eisenstein prime with no imaginary part, a self number,[19] and the sum of nine consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).

480s

[edit]

480

[edit]

480 = 25 × 3 × 5. It is a highly totient number,[37] a refactorable number,[33] a Harshad number, a largely composite number,[75] the sum of a twin prime pair (239 + 241), and the sum of four consecutive primes (109 + 113 + 127 + 131).

is prime[21]

481

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481 = 13 × 37. It is an octagonal number,[15] a centered square number,[30] and a Harshad number.

482

[edit]

482 = 2 × 241. It is a nontotient and a noncototient. There are 482 series-reduced planted trees with 15 nodes.[76]

483

[edit]

483 = 3 × 7 × 23. It is a sphenic number and a Smith number.[44]

484

[edit]

484 = 22 × 112 = 222. It is a palindromic square and a nontotient.

485

[edit]

485 = 5 × 97. There are 485 triangles (of all sizes, including holes) in Sierpiński's triangle after 5 inscriptions[77]

486

[edit]

486 = 2 × 35. It is a Harshad number and a Perrin number.[78]

487

[edit]

It is a prime number, a Chen prime,[1] and the sum of three consecutive primes (157 + 163 + 167).

The only primes under 7.74 × 1013 that divide their own decimal repetends are 3, 487, and 56598313.[79]

488

[edit]

488 = 23 × 61. It is a nontotient and a refactorable number.[33] There are 488 surface points on a cube with edge-length 10.[80]

φ(488) = φ(σ(488)),[70]

489

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489 = 3 × 163. It is an octahedral number.[81]

490s

[edit]

490

[edit]

490 = 2 × 5 × 72. It is a noncototient, a self number,[19] and the sum of the totient function for the first 40 integers. There are 490 integer partitions of 19.[82]

A (possibly arbitrary) large number in the Christian Gospel of Matthew. In Matthew 18:21–35, Jesus tells the Parable of the Unforgiving Servant, instructing Peter to forgive his brother "seventy times seven" times when his brother sins against him [1].

491

[edit]

491 is a prime number, an isolated prime, a Sophie Germain prime,[28] a Chen prime,[1] an Eisenstein prime with no imaginary part, and a strictly non-palindromic number.[45]

492

[edit]

492 = 22 × 3 × 41. It is a refactorable number[33] and the sum of six consecutive primes (71 + 73 + 79 + 83 + 89 + 97). It forms a Ruth–Aaron pair with 493 under first definition.

493

[edit]

493 = 17 × 29. It is the sum of seven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83). It forms a Ruth–Aaron pair with 492 under first definition. The 493d centered octagonal number is also a centered square number.[83]

494

[edit]

494 = 2 × 13 × 19 = .[84] It is a sphenic number and a nontotient.

495

[edit]
Main article: 495 (number)

496

[edit]
Main article: 496 (number)

497

[edit]

497 = 7 × 71. It is a lazy caterer number[12] and the sum of five consecutive primes (89 + 97 + 101 + 103 + 107).

498

[edit]

498 = 2 × 3 × 83. It is a sphenic number, an untouchable number,[16] an admirable number,[85] and an abundant number

499

[edit]

499 is a prime number, an isolated prime, and a Chen prime.[1]

4499 - 3499 is prime.

References

[edit]
  1. ^ a b c d e f g h i j k l Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ a b c d e f g h i j k l m n Sloane, N. J. A. (ed.). "Sequence A028442 (Numbers n such that Mertens' function is zero)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ a b Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A008406 (Triangle T(n,k) read by rows, giving number of graphs with n nodes (n >= 1) and k edges (0 <= k <= n(n-1)/2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A083815 (Semiprimes whose prime factors are distinct and the reversal of one factor is equal to the other)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A345170 (Number of integer partitions of n with an alternating permutation)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Wiener, Anna. "Page Not Found: A Brief History of the 404 Error". Wired. ISSN 1059-1028. Retrieved 2024-12-05.
  9. ^ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A060544 (Centered 9-gonal (also known as nonagonal or enneagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A000930 (Narayana's cows sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A005188 (Armstrong (or Plus Perfect, or narcissistic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^ Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  15. ^ a b Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  17. ^ a b Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  19. ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A003052 (Self numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A047993 (Number of balanced partitions of n: the largest part equals the number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ a b c Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^ Sloane, N. J. A. (ed.). "Sequence A002104 (Logarithmic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A080040 (a(n) = 2*a(n-1) + 2*a(n-2) for n > 1; a(0)=2, a(1)=2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers: products of 3 distinct primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. ^ Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  26. ^ Conway, John H.; Guy, Richard (2012). The Book of Numbers. Springer. p. 39. doi:10.1007/978-1-4612-4072-3. ISBN 978-1-4612-4072-3. OCLC 39220031.
  27. ^ Sloane, N. J. A. (ed.). "Sequence A040017 (Unique period primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-20.
    That number is 142,857,157,142,857,142,856,999,999,985,714,285,714,285,857,142,857,142,855,714,285,571,428,571,428,572,857,143.
  28. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  29. ^ Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  30. ^ a b Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  31. ^ a b Sloane, N. J. A. (ed.). "Sequence A014206 (a(n) = n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ^ Sloane, N. J. A. (ed.). "Sequence A004148 (Generalized Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  33. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  34. ^ a b Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. ^ Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  36. ^ Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  37. ^ a b Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  38. ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  39. ^ Sloane, N. J. A. (ed.). "Sequence A003154 (Centered 12-gonal numbers. Also star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  40. ^ a b Sloane, N. J. A. (ed.). "Sequence A000096 (a(n) = n*(n+3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  41. ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  42. ^ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
  43. ^ Sloane, N. J. A. (ed.). "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  44. ^ a b c Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  45. ^ a b Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  46. ^ Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  47. ^ Sloane, N. J. A. (ed.). "Sequence A070765 (Number of polyiamonds with n cells, without holes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  48. ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  49. ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  50. ^ Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  51. ^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  52. ^ Sloane, N. J. A. (ed.). "Sequence A062786 (Centered 10-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  53. ^ Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  54. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  55. ^ Sloane, N. J. A. (ed.). "Sequence A111441 (Numbers k such that the sum of the squares of the first k primes is divisible by k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  56. ^ Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  57. ^ Grant, Kenneth (1977). Nightside of Eden. London: Frederick Muller Limited. p. 119. ISBN 0-584-10206-2.
  58. ^ Sloane, N. J. A. (ed.). "Sequence A018818 (Number of partitions of n into divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  59. ^ Sloane, N. J. A. (ed.). "Sequence A045943 (Triangular matchstick numbers: a(n) = 3*n*(n+1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  60. ^ Sloane, N. J. A. (ed.). "Sequence A051624 (12-gonal (or dodecagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  61. ^ Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  62. ^ Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  63. ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  64. ^ Sloane, N. J. A. (ed.). "Sequence A091191 (Primitive abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  65. ^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  66. ^ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
  67. ^ a b Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  68. ^ Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  69. ^ Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  70. ^ a b Sloane, N. J. A. (ed.). "Sequence A006872 (Numbers k such that phi(k) = phi(sigma(k)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  71. ^ Sloane, N. J. A. (ed.). "Sequence A045846 (Number of distinct ways to cut an n X n square into squares with integer sides)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  72. ^ Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  73. ^ Sloane, N. J. A. (ed.). "Sequence A111592 (Admirable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  74. ^ Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  75. ^ Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  76. ^ Sloane, N. J. A. (ed.). "Sequence A001678 (Number of series-reduced planted trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  77. ^ Sloane, N. J. A. (ed.). "Sequence A048473 (a(0)=1, a(n) = 3*a(n-1) + 2; a(n) = 2*3^n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  78. ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  79. ^ Sloane, N. J. A. (ed.). "Sequence A045616 (Primes p such that 10^(p-1) == 1 (mod p^2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  80. ^ Sloane, N. J. A. (ed.). "Sequence A005897 (a(n) = 6*n^2 + 2 for n > 0, a(0)=1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  81. ^ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  82. ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) = number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  83. ^ Sloane, N. J. A. (ed.). "Sequence A011900 (a(n) = 6*a(n-1) - a(n-2) - 2 with a(0) = 1, a(1) = 3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  84. ^ Sloane, N. J. A. (ed.). "Sequence A008517 (Second-order Eulerian triangle T(n, k), 1 <= k <= n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  85. ^ Sloane, N. J. A. (ed.). "Sequence A111592 (Admirable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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