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

← 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
Binary1100100002
Ternary1122113
Senary15046
Octal6208
Duodecimal29412
Hexadecimal19016
Hebrewת (Tav)

Mathematical properties edit

400 is the square of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7 (1111).

A circle is divided into 400 grads, which is equal to 360 degrees and 2π radians. (Degrees and radians are the SI accepted units).

400 is a self number in base 10, since there is no integer that added to the sum of its own digits results in 400. On the other hand, 400 is divisible by the sum of its own base 10 digits, making it a Harshad number.

Other fields edit

Four hundred is also

  • .400 (2 hits out of 5 at-bats) is a numerically significant annual batting average statistic in Major League Baseball, last accomplished by Ted Williams of the Boston Red Sox in 1941.
  • The number of days in a Gregorian calendar year changes according to a cycle of exactly 400 years, of which 97 are leap years and 303 are common.
  • The Sun is approximately 400 times the size of the Moon but is also approximately 400 times farther away from Earth than the Moon is, thus creating the illusion in which the Sun and the Moon in Earth's sky appear to be of similar size.[1]
  • In gematria 400 is the largest single number that can be represented without using the Sophit forms (see Kaph, Mem, Nun, Pe, and Tzade).

Integers from 401 to 499 edit

400s edit

401 edit

401 is a prime number, tetranacci number,[2] Chen prime,[3] prime index prime

402 edit

402 = 2 × 3 × 67, sphenic number, nontotient, Harshad number, number of graphs with 8 nodes and 9 edges[6]

403 edit

403 = 13 × 31, heptagonal number, Mertens function returns 0.[4]

404 edit

404 = 22 × 101, Mertens function returns 0,[4] nontotient, noncototient, number of integer partitions of 20 with an alternating permutation.[8]

405 edit

405 = 34 × 5, Mertens function returns 0,[4] Harshad number, pentagonal pyramidal number;

406 edit

406 = 2 × 7 × 29, sphenic number, triangular number, centered nonagonal number,[9] nontotient

  • 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.
  • Peugeot 406 car.
  • Area code for all of Montana.

407 edit

407 = 11 × 37,

  • sum of cubes of 4, 0 and 7 (43 + 03 + 73 = 407); narcissistic number[10]
  • sum of three consecutive primes (131 + 137 + 139)
  • Mertens function returns 0[4]
  • Harshad number
  • lazy caterer number (sequence A000124 in the OEIS)
  • HTTP status code for "Proxy Authentication Required"
  • Area code for Orlando, Florida
  • Colloquial name for the Express Toll Route in Ontario

408 edit

408 = 23 × 3 × 17

409 edit

409 is a prime number, Chen prime,[3] centered triangular number.[14]

410s edit

410 edit

410 = 2 × 5 × 41, sphenic number, sum of six consecutive primes (59 + 61 + 67 + 71 + 73 + 79), nontotient, Harshad number, number of triangle-free graphs on 8 vertices[16]

411 edit

411 = 3 × 137, self number,[17]

412 edit

412 = 22 × 103, nontotient, noncototient, 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, Mertens function returns 0,[4] self number,[17] Blum integer

414 edit

414 = 2 × 32 × 23, Mertens function returns 0,[4] nontotient, Harshad number, number of balanced partitions of 31[18]

  is prime[19]

415 edit

415 = 5 × 83, logarithmic number[20]

  • HTTP status code for "Unsupported Media Type"
  • 415 Records, a record label
  • 415 refers to California Penal Code, section 415, pertaining to public fighting, public disturbance, and public use of offensive words likely to provoke an immediate violent reaction.
  • Area code 415, a telephone area code for San Francisco, California

416 edit

416 = 25 × 13, number of independent vertex sets and vertex covers in the 6-sunlet graph[21]

417 edit

417 = 3 × 139, Blum integer

418 edit

418 = 2 × 11 × 19; sphenic number,[22] balanced number.[23] It is also the fourth 71-gonal number.[24]

419 edit

A prime number, Sophie Germain prime,[28] Chen prime, Eisenstein prime with no imaginary part, highly cototient number,[29] Mertens function returns 0[4]

  • refers to the Nigerian advance fee fraud scheme (after the section of the Nigerian Criminal Code it violates)
  • The Area Code for Toledo, OH and other surrounding areas.

420s edit

420 edit

421 edit

422 edit

422 = 2 × 211, Mertens function returns 0,[4] nontotient, since 422 = 202 + 20 + 2 it is the maximum number of regions into which 21 intersecting circles divide the plane.[31]

423 edit

423 = 32 × 47, Mertens function returns 0,[4] Harshad number, number of secondary structures of RNA molecules with 10 nucleotides[32]

424 edit

424 = 23 × 53, sum of ten consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), Mertens function returns 0,[4] refactorable number,[33] self number[17]

425 edit

425 = 52 × 17, pentagonal number,[34] centered tetrahedral number, sum of three consecutive primes (137 + 139 + 149), Mertens function returns 0,[4] 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, sphenic number, nontotient, untouchable number

427 edit

427 = 7 × 61, Mertens function returns 0.[4] 427! + 1 is prime.

428 edit

428 = 22 × 107, Mertens function returns 0, nontotient, 42832 + 1 is prime[35]

429 edit

429 = 3 × 11 × 13, sphenic number, Catalan number[36]

430s edit

430 edit

430 = 2 × 5 × 43, number of primes below 3000, sphenic number, untouchable number[13]

431 edit

A prime number, Sophie Germain prime,[28] sum of seven consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73), Chen prime, prime index prime, Eisenstein prime with no imaginary part

432 edit

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

433 edit

A prime number, Markov number,[38] star number.[39]

  • The perfect score in the game show Fifteen To One, only ever achieved once in over 2000 shows.
  • 433 can refer to composer John Cage's composition 4′33″ (pronounced "Four minutes, thirty-three seconds" or just "Four thirty-three").

434 edit

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

435 edit

435 = 3 × 5 × 29, sphenic number, triangular number, hexagonal number,[41] self number,[17] number of compositions of 16 into distinct parts[42]

436 edit

436 = 22 × 109, nontotient, noncototient, lazy caterer number (sequence A000124 in the OEIS)

437 edit

437 = 19 × 23, Blum integer

438 edit

438 = 2 × 3 × 73, sphenic number, Smith number.[43]

439 edit

A prime number, sum of three consecutive primes (139 + 149 + 151), sum of nine consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), strictly non-palindromic number[44]

440s edit

440 edit

441 edit

441 = 32 × 72 = 212

  • 441 is the sum of the cubes of the first 6 natural numbers (441 = 13 + 23 + 33 + 43 + 53 + 63).
  • 441 is a centered octagonal number,[45] a refactorable number,[33] and a Harshad number.
  • 441 is the number of squares on a Super Scrabble board.

442 edit

442 = 2 × 13 × 17 = 212 + 1,[46] sphenic number, sum of eight consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71)

443 edit

A prime number, Sophie Germain prime,[28] Chen prime, Eisenstein prime with no imaginary part, Mertens function sets new low of -9, which stands until 659.

  • In computing, it is the default port for HTTPS connections.

444 edit

444 = 22 × 3 × 37, refactorable number,[33] Harshad number, number of noniamonds without holes.[47]

445 edit

445 = 5 × 89, number of series-reduced trees with 17 nodes[48]

446 edit

446 = 2 × 223, nontotient, self number[17]

447 edit

447 = 3 × 149, number of 1's in all partitions of 22 into odd parts[49]

448 edit

448 = 26 × 7, untouchable number,[13] refactorable number,[33] Harshad number

449 edit

A prime number, sum of five consecutive primes (79 + 83 + 89 + 97 + 101), Chen prime, Eisenstein prime with no imaginary part, Proth prime.[50] Also the largest number whose factorial is less than 101000

450s edit

450 edit

450 = 2 × 32 × 52, nontotient, sum of totient function for first 38 integers, refactorable number,[33] Harshad number,

451 edit

451 = 11 × 41; 451 is a Wedderburn–Etherington number[51] and a centered decagonal number;[52] its reciprocal has period 10; 451 is the smallest number with this period reciprocal length.

452 edit

452 = 22 × 113, number of surface-points of a tetrahedron with edge-length 15[54]

  • SMTP code meaning that the requested mail action was not carried out because of insufficient system storage

453 edit

453 = 3 × 151, Blum integer

454 edit

454 = 2 × 227, nontotient, a Smith number[43]

455 edit

455 = 5 × 7 × 13, sphenic number, tetrahedral number[55]

456 edit

456 = 23 × 3 × 19, sum of a twin prime (227 + 229), sum of four consecutive primes (107 + 109 + 113 + 127), centered pentagonal number,[57] icosahedral number

457 edit

  • A prime number, sum of three consecutive primes (149 + 151 + 157), self number.[17]
  • The international standard frequency for radio avalanche transceivers (457 kHz).

458 edit

458 = 2 × 229, nontotient, number of partitions of 24 into divisors of 24[58]

459 edit

459 = 33 × 17, triangular matchstick number[59]

460s edit

460 edit

460 = 22 × 5 × 23, centered triangular number,[14] dodecagonal number,[60] Harshad number, sum of twelve consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61)

461 edit

A prime number, Chen prime, sexy prime with 467, Eisenstein prime with no imaginary part, prime index prime

462 edit

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

463 edit

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

464 edit

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

  • In chess it is the number of legal positions of the kings, not counting mirrored positions. Has some importance when constructing an endgame tablebase.
  • Model number of the home computer Amstrad CPC 464.

465 edit

465 = 3 × 5 × 31, sphenic number, triangular number, member of the Padovan sequence,[65] Harshad number

466 edit

466 = 2 × 233, noncototient, lazy caterer number (sequence A000124 in the OEIS)

467 edit

A prime number, safe prime,[66] sexy prime with 461, Chen prime, Eisenstein prime with no imaginary part

  is prime[19]

468 edit

468 = 22 × 32 × 13, sum of ten consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67), refactorable number,[33] self number,[17] Harshad number

469 edit

469 = 7 × 67, centered hexagonal number.[67] 469! - 1 is prime.

470s edit

470 edit

470 = 2 × 5 × 47, sphenic number, nontotient, noncototient, cake number

  • In golf, 470 is the minimum length in yards from the tee to the hole on a Par 5.
  • 470 is an Olympic class of sailing dinghy

471 edit

471 = 3 × 157, sum of three consecutive primes (151 + 157 + 163), perfect totient number,[68] φ(471) = φ(σ(471)).[69]

472 edit

472 = 23 × 59, nontotient, untouchable number,[13] refactorable number,[33] number of distinct ways to cut a 5 × 5 square into squares with integer sides[70]

  • The Amstrad CPC472 was a short-lived home computer for the Spanish market.

473 edit

473 = 11 × 43, sum of five consecutive primes (83 + 89 + 97 + 101 + 103), Blum integer

474 edit

474 = 2 × 3 × 79, sphenic number, sum of eight consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73), nontotient, noncototient, sum of totient function for first 39 integers, untouchable number,[13] nonagonal number[71]

475 edit

475 = 52 × 19, 49-gonal number, member of the Mian–Chowla sequence.[5]

476 edit

476 = 22 × 7 × 17, Harshad number, admirable number[72]

477 edit

477 = 32 × 53, pentagonal number[34]

478 edit

478 = 2 × 239, Companion Pell number, number of partitions of 26 that do not contain 1 as a part[73]

479 edit

A prime number, safe prime,[66] sum of nine consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), Chen prime, Eisenstein prime with no imaginary part, self number[17]

480s edit

480 edit

480 = 25 × 3 × 5, sum of a twin prime (239 + 241), sum of four consecutive primes (109 + 113 + 127 + 131), highly totient number,[37] refactorable number,[33] Harshad number

  is prime[19]

481 edit

481 = 13 × 37, octagonal number,[12] centered square number,[30] Harshad number

482 edit

482 = 2 × 241, nontotient, noncototient, number of series-reduced planted trees with 15 nodes[74]

483 edit

483 = 3 × 7 × 23, sphenic number, Smith number[43]

484 edit

484 = 22 × 112 = 222, palindromic square, nontotient

485 edit

485 = 5 × 97, number of triangles (of all sizes, including holes) in Sierpiński's triangle after 5 inscriptions[75]

486 edit

486 = 2 × 35, Harshad number, Perrin number[76]

487 edit

A prime number, sum of three consecutive primes (157 + 163 + 167), Chen prime,

  • The only primes under 7.74 × 1013 that divide their own decimal repetends are 3, 487, and 56598313.[77]
  • Shorthand for the Intel 80487 floating point processor chip.

488 edit

488 = 23 × 61, nontotient, refactorable number,[33] φ(488) = φ(σ(488)),[69] number of surface points on a cube with edge-length 10.[78]

489 edit

489 = 3 × 163, octahedral number[79]

490s edit

490 edit

490 = 2 × 5 × 72, noncototient, sum of totient function for first 40 integers, number of integer partitions of 19,[80] self number.[17]

491 edit

A prime number, isolated prime, Sophie Germain prime,[28] Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number[44]

492 edit

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

493 edit

493 = 17 × 29, sum of seven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83), member of a Ruth–Aaron pair with 492 under first definition, the 493d centered octagonal number is also a centered square number[81]

494 edit

494 = 2 × 13 × 19 =  ,[82] sphenic number, nontotient

495 edit

496 edit

497 edit

497 = 7 × 71, sum of five consecutive primes (89 + 97 + 101 + 103 + 107), lazy caterer number (sequence A000124 in the OEIS)

498 edit

498 = 2 × 3 × 83, sphenic number, untouchable number,[13] admirable number,[83] abundant number

499 edit

A prime number, isolated prime, Chen prime, 4499 - 3499 is prime

References edit

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  4. ^ a b c d e f g h i j k l m n "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  5. ^ a b "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
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  8. ^ 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.
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  15. ^ "Venice: The City Built on Water". Google Maps. Retrieved 2022-09-21.
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  19. ^ 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. Retrieved 2022-06-02.
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  21. ^ Sloane, N. J. A. (ed.). "Sequence A080040". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^ Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers: products of 3 distinct primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-07-02.
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    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.
  26. ^ L. Masinter (1 April 1998). "Hyper Text Coffee Pot Control Protocol (HTCPCP/1.0)". Network Working Group (RFC). doi:10.17487/RFC2324. Retrieved 13 Sep 2018. Any attempt to brew coffee with a teapot should result in the error code "418 I'm a teapot". The resulting entity body MAY be short and stout.
  27. ^ I. Nazar (1 April 2014). "The Hyper Text Coffee Pot Control Protocol for Tea Efflux Appliances (HTCPCP-TEA)". IETF Request for Comments (RFC) Pages - Test (RFC). doi:10.17487/RFC7168. ISSN 2070-1721. Retrieved 13 Sep 2018. TEA-capable pots that are not provisioned to brew coffee may return either a status code of 503, indicating temporary unavailability of coffee, or a code of 418 as defined in the base HTCPCP specification to denote a more permanent indication that the pot is a teapot.
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  51. ^ "Sloane's A001190 : Wedderburn-Etherington numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  52. ^ "Sloane's A062786 : Centered 10-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  53. ^ "451 Unavailable For Legal Reasons - HTTP | MDN". developer.mozilla.org. Retrieved 2021-04-23.
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  55. ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
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  57. ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  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". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  60. ^ "Sloane's A051624 : 12-gonal (or dodecagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  61. ^ "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  62. ^ "Sloane's A036913 : Sparsely totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  63. ^ "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  64. ^ "Sloane's A091191 : Primitive abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  65. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  66. ^ a b "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  67. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  68. ^ "Sloane's A082897 : Perfect totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  69. ^ a b Sloane, N. J. A. (ed.). "Sequence A006872". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  70. ^ 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. Retrieved 2022-05-23.
  71. ^ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  72. ^ Sloane, N. J. A. (ed.). "Sequence A111592 (Admirable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  73. ^ 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. Retrieved 2022-06-02.
  74. ^ 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.
  75. ^ Sloane, N. J. A. (ed.). "Sequence A048473". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  76. ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  77. ^ "Sloane's A045616 : Primes p such that 10^(p-1) == 1 (mod p^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2018-05-31.
  78. ^ Sloane, N. J. A. (ed.). "Sequence A005897". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  79. ^ "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  80. ^ "Sloane's A000041 : a(n) = number of partitions of n (the partition numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.
  81. ^ Sloane, N. J. A. (ed.). "Sequence A011900". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  82. ^ Sloane, N. J. A. (ed.). "Sequence A008517". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  83. ^ "Sloane's A111592 : Admirable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-10.