550 (number)

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← 499 500 501 →
Cardinalfive hundred
Ordinal500th
(five hundredth)
Factorization22 × 53
Greek numeralΦ´
Roman numeralD
Binary1111101002
Ternary2001123
Senary21526
Octal7648
Duodecimal35812
Hexadecimal1F416
ArmenianՇ
Hebrewת"ק / ך
Babylonian cuneiform𒐜⟪
Egyptian hieroglyph𓍦

500 (five hundred) is the natural number following 499 and preceding 501.

Mathematical properties

500 = 22 × 53. It is an Achilles number, meaning that it is divisible by the squares of its prime factors (i.e. 4 and 25) but is not a power itself, and a Harshad number, meaning it is divisible by the sum of its digits. It is the number of planar partitions of 10.[1]

Other fields

Five hundred is also

Slang names

  • Monkey (UK slang for £500; US slang for $500)[2]

Integers from 501 to 599

500s

501

502

502 = 2 × 251. It is a vertically symmetric number.[3]

503

503 is a prime number, a safe prime,[4] a Chen prime,[5] an Eisenstein prime with no imaginary part,[6] an index of a prime Lucas number,[7] and an isolated prime. It is the sum of three consecutive primes (163 + 167 + 173)[8] and the sum of the cubes of the first four primes.[9]

504

504 = 23 × 32 × 7. It is a tribonacci number,[10] a semi-meandric number, a refactorable number,[11] a Harshad number and a largely composite number.[12] It is the sum of the smallest pair of amicable numbers: (220, 284).[13] The group order of the fourth smallest non-cyclic simple group, A1(8) = 2G2(3)′, is 504. There are 504 symmetries of the simple group PSL(2,8) that is the automorphism group of the Macbeath surface.[14]

∑ n = 0 10 504 n {\displaystyle \sum _{n=0}^{10}{504}^{n}} {\displaystyle \sum _{n=0}^{10}{504}^{n}} is prime.[15]

505

505 = 5 × 101. It is the magic constant of n×n normal magic square and n-queens problem for n = 10.

506

506 = 2 × 11 × 23. It is a sphenic number, a square pyramidal number,[16] a pronic number,[17] a Harshad number.

10 506 − 10 253 − 1 {\displaystyle 10^{506}-10^{253}-1} {\displaystyle 10^{506}-10^{253}-1} is a prime number. Its decimal expansion is 252 nines, an eight, and 253 more nines.

507

507 = 3 × 132. it is a central polygonal number because 507=232 - 23 + 1.[18]

508

508 = 22 × 127. It is the sum of four consecutive primes (113 + 127 + 131 + 137). There are 508 graphical forest partitions of 30.[19] Since 508 = 222 + 22 + 2, it is the maximum number of regions into which 23 intersecting circles divide the plane.[20]

509

509 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, a highly cototient number[21] and a prime index prime.

It is a Sophie Germain prime, additionally, it is the smallest Sophie Germain prime to start a 4-term Cunningham chain of the first kind {509, 1019, 2039, 4079}.

510s

510

510 = 2 × 3 × 5 × 17. It is a nontotient, a sparsely totient number,[22] and a Harshad number. There are 510 nonempty proper subsets of an 9-element set.[23]

It is the sum of eight consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79), the sum of ten consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71), and the sum of twelve consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).

511

512

513

513 = 33 × 19. It is a Harshad number and a Leyland number of the second kind,[24] using 3 & 6 (36 - 63). It is palindromic in bases 2 (10000000012) and 8 (10018).

514

514 = 2 × 257. It is a centered triangular number[25] and a nontotient. It is a palindrome in bases 4 (200024), 16 (20216), and 19 (18119).

515

515 = 5 × 103. It is the sum of nine consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73). There are 515 complete compositions of 11.[26]

516

516 = 22 × 3 × 43. It is a nontotient, an untouchable number,[27] a refactorable number,[11] and a Harshad number.

517

517 = 11 × 47. It is a Smith number[28] and the sum of five consecutive primes (97 + 101 + 103 + 107 + 109).

518

518 = 2 × 7 × 37. It is a sphenic number, a nontotient, an untouchable number,[27] and a Harshad number. It is arepdigit and thus palindromic in bases 6 (22226) and 36 (EE36).

518= 51 + 12 + 83, a property shared with 175 and 598.

519

519 = 3 × 173. It is palindromic in bases 9 (6369) and 12 (37312), and it is a D-number.[29] It is the sum of three consecutive primes (167 + 173 + 179).

520s

520

520 = 23 × 5 × 13. It is an untouchable number,[27] an idoneal number, and a palindromic number in base 14 (29214).

521

521 is a prime number, a Lucas prime.[30] a Chen prime, and an Eisenstein prime with no imaginary part. It is palindromic in bases 11 (43411) and 20 (16120).

It is a Mersenne exponent, i.e. 2521−1 is prime. It is the largest known such exponent that is the lesser of twin primes.[31]

4521 - 3521 is prime.

522

522 = 2 × 32 × 29. It is a repdigit in bases 28 (II28) and 57 (9957) and a Harshad number. It is the sum of six consecutive primes (73 + 79 + 83 + 89 + 97 + 101).

There are 522 series-parallel networks with 8 unlabeled edges.[32]

523

523 is a prime number and a prime with a prime number of prime digits.[33] It is palindromic in bases 13 (31313) and 18 (1B118). It is the smallest prime number that starts a prime gap of length greater than 14. It is the sum of seven consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89).

524

524 = 22 × 131. There are 524 partitions of 44 into powers of 2.[34]

525

525 = 3 × 52 × 7. It is a self number, [35] and it is palindromic in base ten.

It is the sum of all prime numbers that divide the orders of the twenty-six sporadic groups (2, 3, 5, ..., 71; aside from 53 and 61).[36]

It is the sum of the dimensions of all five exceptional Lie algebras (14, 52, 78, 133, 248).[37]

526

526 = 2 × 263. It is a centered pentagonal number,[38] a nontotient, and a Smith number.[28]

527

527 = 17 × 31. It is palindromic in base 15 (25215).

There are 527 diagonals in a 34-gon[39]

528

528 = 24 × 3 × 11. It is palindromic in bases 9 (6469) and 17 (1E117). It is the 32nd triangular number,[40] and the 167th Totient number.[41]

529

529 = 232. It is a centered octagonal number[42] and a lazy caterer number.[43]

530s

530

530 = 2 × 5 × 53. It is an untouchable number,[27] a sphenic number, and a nontotient. It is palindromic in bases 4 (201024), 16 (21216), and 23 (10123). It is the sum of totient function for first 41 integers and the sum of the first three perfect numbers.

531

531 = 32 × 59. It is palindromic in base 12 (38312) and a Harshad number.

There are 531 symmetric matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to 6.[44]

532

532 = 22 × 7 × 19. It is a pentagonal number,[45] a nontotient, and an admirable number. It is a repdigit and thus palindromic in bases 11 (44411), 27 (JJ27), and 37 (EE37).

533

533 = 13 × 41. It is palindromic in base 19 (19119) and a generalized octagonal number.[46] It is the sum of three consecutive primes (173 + 179 + 181) and the sum of five consecutive primes (101 + 103 + 107 + 109 + 113).

534

534 = 2 × 3 × 89. It is a sphenic number, a nontotient and an admirable number. It is palindromic in bases 5 (41145) and 14 (2A214). It is the sum of four consecutive primes (127 + 131 + 137 + 139).

∑ n = 0 10 534 n {\displaystyle \sum _{n=0}^{10}{534}^{n}} {\displaystyle \sum _{n=0}^{10}{534}^{n}} is prime[15]

535

535 = 5 × 107. It is a Smith number.[28]

34 n 3 + 51 n 2 + 27 n + 5 = 535 {\displaystyle 34n^{3}+51n^{2}+27n+5=535} {\displaystyle 34n^{3}+51n^{2}+27n+5=535} for n = 2 {\displaystyle n=2} {\displaystyle n=2}; this polynomial plays an essential role in Apéry's proof that ζ ( 3 ) {\displaystyle \zeta (3)} {\displaystyle \zeta (3)} is irrational.

535 is used as an abbreviation for May 35, which is used in China instead of June 4 to evade censorship by the Chinese government of references on the Internet to the Tiananmen Square protests of 1989.[47]

536

536 = 23 × 67. It is a refactorable number,[11] the 168th Totient number,[48] and the lowest happy number beginning with the digit 5.

There are 536 ways to arrange the pieces of the ostomachion into a square, not counting rotation or reflection.

There are 536 1's in all partitions of 23 into odd parts.[49]

537

537 = 3 × 179. It is a Blum integer, a D-number,[29] and a zero of the Mertens function.

538

538 = 2 × 269. It is a nontotient and an open meandric number.

Other fields:

There are a total of 538 votes in the United States Electoral College. The US political news site, FiveThirtyEight, is a reference to the electoral college.

Radio 538 is a Dutch commercial radio station.

539

539 = 72 × 11.

∑ n = 0 10 539 n {\displaystyle \sum _{n=0}^{10}{539}^{n}} {\displaystyle \sum _{n=0}^{10}{539}^{n}} is prime.[15]

540s

540

540 = 22 × 33 × 5. It is a largely composite number,[12] an untouchable number,[27] a heptagonal number, and a decagonal number.[50]

It is the sum of a pair of twin primes (269 + 271) and a repdigit in bases 26 (KK26), 29 (II29), 35 (FF35), 44 (CC44), 53 (AA53), and 59 (9959).

541

541 is the 100th prime, a lucky prime, [51] a Chen prime, a zero of the Mertens function and a star number.[52] It is palindromic in bases 18 (1C118) and 20 (17120). It is the fifth ordered Bell number that represents the number of ordered partitions of [ 5 ] {\displaystyle [5]} {\displaystyle [5]}.[53]

4541 - 3541 is prime.[54]

542

542 = 2 × 271. It is a nontotient and the sum of totient function for the first 42 integers.[55]

543

543 = 3 × 181. It is palindromic in bases 11 (45411) and 12 (39312) and a D-number.[29]

∑ n = 0 10 543 n {\displaystyle \sum _{n=0}^{10}{543}^{n}} {\displaystyle \sum _{n=0}^{10}{543}^{n}} is prime[15]

544

544 = 25 × 17. Take a grid of 2 times 5 points. There are 14 points on the perimeter. Join every pair of the perimeter points by a line segment. The lines do not extend outside the grid. 544 is the number of regions formed by these lines. (sequence A331452 in the OEIS)

544 is also the number of pieces that could be seen in a 5×5×5×5 Rubik's Tesseract. As a standard 5×5×5 has 98 visible pieces (53 − 33), a 5×5×5×5 has 544 visible pieces (54 − 34).

545

545 = 5 × 109. It is a centered square number[56], and it is palindromic in bases 10 (54510) and 17 (1F117).

546

546 = 2 × 3 × 7 × 13. It is a repdigit in bases 9 and 16, and it is palindromic in bases 4 (202024), 9 (6669), and 16 (22216). It is the sum of eight consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).

546! − 1 is prime.

547

547 is a prime number, a cuban prime,[57] a centered hexagonal number,[58] a centered heptagonal number,[59] and a prime index prime.

548

548 = 22 × 137. It is a nontotient. Every positive integer is the sum of at most 548 ninth powers.

549

549 = 32 × 61. It is a repdigit in bases 13 (33313) and 60 (9960).

φ(549) = φ(σ(549)).[60]

550s

550

550 = 2 × 52 × 11. It is a pentagonal pyramidal number,[61] a primitive abundant number,[62] a nontotient, and a Harshad number. It is a repdigit in bases 24 (MM24), 49 (BB49), and 54 (AA54).

551

551 = 19 × 29. It is palindromic in base 22 (13122) and the sum of three consecutive primes (179 + 181 + 191).

There are 551 mathematical trees on 12 unlabeled nodes.[63]

552

552 = 23 × 3 × 23. It is a pronic number,[17] an untouchable number, and a Harshad number.[27] It is palindromic in base 19 (1A119). It is the sum of six consecutive primes (79 + 83 + 89 + 97 + 101 + 103) and the sum of ten consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).

There are 552 prime knots with 11 crossings.[64]

553

553 = 7 × 79. It is a central polygonal number[18] and the sum of nine consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).

554

554 = 2 × 277. It is a nontotient and a 2-Knödel number.

Mertens function(554) = 6, a record high that stands until 586.

555

556

556 = 22 × 139. It is a happy number and an untouchable number, because it is never the sum of the proper divisors of any integer.[27] It is the sum of four consecutive primes (131 + 137 + 139 + 149).

557

557 is a prime number, a Chen prime, and an Eisenstein prime with no imaginary part.

There are 557 parallelogram polyominoes with 9 cells.[65]

558

558 = 2 × 32 × 31. It is a nontotient, a Harshad number, and a repdigit in bases 30 (II30) and 61 (9961).

559

559 = 13 × 43. It is a nonagonal number[66] and a centered cube number.[67] It is palindromic in base 18 (1D118). It is the sum of five consecutive primes (103 + 107 + 109 + 113 + 127) and the sum of seven consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97).

560s

560

560 = 24 × 5 × 7. It is a tetrahedral number,[68] an octagonal number, and a refactorable number. It is palindromic in bases 3 (2022023) and 6 (23326). There are 560 diagonals in a 35-gon.[39]

561

561 = 3 × 11 × 17. It is a sphenic number, a hexagonal number,[69] the 33rd triangular number,[70] and the first Carmichael number.[71] It is palindromic in bases 2 (10001100012) and 20 (18120).

562

562 = 2 × 281. It is a Smith number,[28] an untouchable number.[27] and a a lazy caterer number.[72] It is palindromic in bases 4 (203024), 13 (34313), 14 (2C214), 16 (23216), and 17 (1G117). It is the sum of twelve consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).

56264 + 1 is prime

563

563 is a prime number a safe prime,[4] a Chen prime, an Eisenstein prime with no imaginary part, a balanced prime,[73] a sexy prime, a happy prime, a prime index prime, and a strictly non-palindromic number.[74] It is the largest known Wilson prime.[75]

5563 - 4563 is prime.[76]

564

564 = 22 × 3 × 47. It is a refactorable number and the sum of a pair of twin primes (281 + 283). It is palindromic in bases 5 (42245) and 9 (6869). There are 564 primes less than or equal to 212.[77]

565

565 = 5 × 113. It is a member of the Mian–Chowla sequence[78] and a happy number. It is palindromic in bases 10 (56510) and 11 (47411). It is the sum of three consecutive primes (181 + 191 + 193).

566

566 = 2 × 283. It is a nontotient, a happy number, and a 2-Knödel number.

567

567 = 34 × 7. It is palindromic in base 12 (3B312).

∑ n = 0 10 567 n {\displaystyle \sum _{n=0}^{10}{567}^{n}} {\displaystyle \sum _{n=0}^{10}{567}^{n}} is prime[15]

568

568 = 23 × 71. It is a refactorable number, and it is palindromic in bases 7 (14417) and 21 (16121). It is the sum of the first nineteen primes.[79] It is the smallest number whose seventh power is the sum of 7 seventh powers.

There are 568 millilitres in an imperial pint.

569

569 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, and a strictly non-palindromic number.[74]

570s

570

570 = 2 × 3 × 5 × 19. It is a triangular matchstick number[80] and a balanced number.[81]

571

571 is a prime number, a Chen prime, and a centered triangular number.[25] There are 571 domino tilings of a 3x10 rectangle.

572

572 = 22 × 11 × 13. It is a primitive abundant number[62] and a nontotient. It is palindromic in bases 3 (2100123) and 15 (28215).

573

573 = 3 × 191. It is a Blum integer.

It is known as the Konami number, since "ko-na-mi" is associated with 573 in the Japanese wordplay Goroawase.

574

574 = 2 × 7 × 41. It is a sphenic number and a nontotient. It is palindromic in base 9 (7079). There are 574 partitions of 27 that do not contain 1 as a part.[82]

There are 574 amino acid residues in a hemoglobin molecule.

575

575 = 52 × 23. It is palindromic in bases 10 (57510) and 13 (35313), and it is a centered octahedral number.[83]

The sum of the squares of the first 575 primes is divisible by 575.[84]

576

576 = 26 × 32 = 242. It is a highly totient number,[85] a Smith number,[28] an untouchable number,[27] a Harshad number, and a cake number. It is the sum of four consecutive primes (137 + 139 + 149 + 151). It is palindromic in bases 11 (48411), 14 (2D214), and 23 (12123). There are 576 parts in all compositions of 8.[86]

577

577 is a prime number, a Proth prime,[87] and a Chen prime. It is palindromic in bases 18 (1E118) and 24 (10124).

578

578 = 2 × 172. It is palindromic in base 16 (24216), and it is a nontotient. The area of a square with diagonal 34[88] is 578.

579

579 = 3 × 193. It is a semiprime and a ménage number.[89]

580s

580

580 = 22 × 5 × 29. It is palindromic in bases 12 (40412) and 17 (20217), and it is the sum of six consecutive primes (83 + 89 + 97 + 101 + 103 + 107).

581

581 = 7 × 83. It is a Blum integer and the sum of three consecutive primes (191 + 193 + 197).

582

582 = 2 × 3 × 97. It is a sphenic number, a nontotient, a vertically symmetric number,[90] and an admirable number. It is the sum of eight consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89).

583

583 = 11 × 53. It is palindromic in base 9 (7179). There are 583 compositions of 11 whose run-lengths are either weakly increasing or weakly decreasing.[91]

584

584 = 23 × 73. It is an untouchable number,[27] a refactorable number and the sum of totient function for first 43 integers.

585

585 = 32 × 5 × 13. It is palindromic in bases 2 (10010010012), 8 (11118), and 10 (58510). It is a repdigit in bases 8, 38, 44, and 64. It is the sum of powers of 8 from 0 to 3.

When counting in binary with fingers, expressing 585 as 1001001001, results in the isolation of the index and little fingers of each hand, "throwing up the horns".

586

586 = 2 × 293. It is a 2-Knödel number.

Mertens function(586) = 7 a record high that stands until 1357.

587

587 is a prime number, a safe prime,[4] a Chen prime, an Eisenstein prime with no imaginary part, and a prime index prime. It is the sum of five consecutive primes (107 + 109 + 113 + 127 + 131). It is palindromic in bases 11 (49411) and 15 (29215).

588

588 = 22 × 3 × 72. It is a Smith number[28] and a Harshad number. It is palindromic in base 13 (36313).

589

589 = 19 × 31. It is a centered tetrahedral number and the sum of three consecutive primes (193 + 197 + 199). It is palindromic in base 21 (17121).

590s

590

590 = 2 × 5 × 59. It is a sphenic number, a pentagonal number,[45] and a nontotient. It is palindromic in base 19 (1C119).

591

591 = 3 × 197. It is a D-number[29]

592

592 = 24 × 37. It is a Harshad number. It is palindromic in bases 9 (7279) and 12 (41412).

59264 + 1 is prime

593

593 is a prime number. a Sophie Germain prime, an Eisenstein prime with no imaginary part, a balanced prime,[73] a Leyland prime[92] using 2 & 9 (29 + 92), a member of the Mian–Chowla sequence,[78] and a strictly non-palindromic number.[74] It is the sum of seven consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101) and the sum of nine consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).

594

594 = 2 × 33 × 11. It is a nontotient, a Harshad number, and a balanced number.[81] It is palindromic in bases 5 (43345) and 16 (25216). It is the sum of ten consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79). There are 594 of diagonals in a 36-gon.[39]

595

595 = 5 × 7 × 17. It is a sphenic number, a centered nonagonal number,[93] and the 34th triangular number.[70] It is palindromic in bases 10 (59510) and 18 (1F118).

596

596 = 22 × 149. It is a nontotient and a lazy caterer number.[94] It is the sum of four consecutive primes (139 + 149 + 151 + 157).

597

597 = 3 × 199. It is a Blum integer

598

598 = 2 × 13 × 23 = 51 + 92 + 83. It is palindromic in bases 4 (211124) and 11 (4A411), and it is a sphenic number. There are 598 non-alternating permutations of {1...6}.

599

599 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, and a prime index prime.

4599 - 3599 is prime.

References

  1. Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. Evans, I.H., Brewer's Dictionary of Phrase and Fable, 14th ed., Cassell, 1990, ISBN 0-304-34004-9
  3. "A053701 - OEIS". oeis.org. Retrieved June 28, 2026.
  4. Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  5. since 503+2 is a product of two primes, 5 and 101
  6. since it is a prime which is congruent to 2 modulo 3.
  7. Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. that is, a term of the sequence OEIS: A034961
  9. that is, the first term of the sequence OEIS: A133525
  10. Sloane, N. J. A. (ed.). "Sequence A000073 (Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  11. Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  12. Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. Sloane, N. J. A. (ed.). "Sequence A259180 (Amicable pairs.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 22, 2024.
  14. Wohlfahrt, K. (1985). "Macbeath's curve and the modular group". Glasgow Math. J. 27: 239–247. doi:10.1017/S0017089500006212. MR 0819842.
  15. 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 June 2, 2022.
  16. Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  17. Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  18. Sloane, N. J. A. (ed.). "Sequence A002061". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  19. Sloane, N. J. A. (ed.). "Sequence A000070". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2022.
  20. Sloane, N. J. A. (ed.). "Sequence A014206". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  22. Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  23. Sloane, N. J. A. (ed.). "Sequence A000918". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. Sloane, N. J. A. (ed.). "Sequence A045575 (Leyland numbers of the second kind)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  26. Sloane, N. J. A. (ed.). "Sequence A107429 (Number of complete compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  27. Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  28. Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  29. Sloane, N. J. A. (ed.). "Sequence A033553 (3-Knödel numbers or D-numbers: numbers n > 3 such that n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2022.
  30. Sloane, N. J. A. (ed.). "Sequence A005479 (Prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  31. Dr. Kirkby (May 19, 2021). "Many more twin primes below Mersenne exponents than above Mersenne exponents". Mersenne Forum.
  32. Sloane, N. J. A. (ed.). "Sequence A000084 (Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  33. Sloane, N. J. A. (ed.). "Sequence A348699 (Primes with a prime number of prime digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  34. Sloane, N. J. A. (ed.). "Sequence A000123 (Number of binary partitions: number of partitions of 2n into powers of 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. Sloane, N. J. A. (ed.). "Sequence A003052 (Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved January 9, 2024.
  36. Sloane, N. J. A. (ed.). "Sequence A329191 (The prime divisors of the orders of the sporadic finite simple groups.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved January 9, 2024.
  37. Sloane, N. J. A. (ed.). "Sequence A113907 (Dimensions of the five sporadic Lie groups.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved January 9, 2024.
  38. Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  39. Sloane, N. J. A. (ed.). "Sequence A000096". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2022.
  40. "A000217 - OEIS". oeis.org. Retrieved November 27, 2024.
  41. "A002202 - OEIS". oeis.org. Retrieved November 27, 2024.
  42. 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. Retrieved June 11, 2016.
  43. "A000124 - OEIS". oeis.org. Retrieved June 28, 2026.
  44. Sloane, N. J. A. (ed.). "Sequence A138178 (Number of symmetric matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  45. Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  46. Sloane, N. J. A. (ed.). "Sequence A001082 (Generalized octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  47. Larmer, Brook (October 26, 2011). "Where an Internet Joke Is Not Just a Joke". New York Times. Retrieved November 1, 2011.
  48. "A002202 - OEIS". oeis.org. Retrieved November 27, 2024.
  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 A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  51. Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  52. Sloane, N. J. A. (ed.). "Sequence A003154 (Centered 12-gonal numbers. Also star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  53. Sloane, N. J. A. (ed.). "Sequence A000670 (Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved October 23, 2023.
  54. Sloane, N. J. A. (ed.). "Sequence A059801 (Numbers k such that 4^k - 3^k is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved October 23, 2023.
  55. Sloane, N. J. A. (ed.). "Sequence A002088". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  56. Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  57. Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  58. Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  59. Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  60. Sloane, N. J. A. (ed.). "Sequence A006872". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  61. Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  62. Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  63. "Sloane's A000055: Number of trees with n unlabeled nodes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on November 29, 2010. Retrieved December 19, 2021.
  64. Sloane, N. J. A. (ed.). "Sequence A002863 (Number of prime knots with n crossings)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  65. Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  66. Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  67. Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  68. Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  69. Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  70. "A000217 - OEIS". oeis.org. Retrieved November 29, 2024.
  71. Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 14. ISBN 978-1-84800-000-1.
  72. "A000124 - OEIS". oeis.org. Retrieved June 29, 2026.
  73. Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  74. Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  75. Sloane, N. J. A. (ed.). "Sequence A007540 (Wilson primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  76. Sloane, N. J. A. (ed.). "Sequence A059802 (Numbers k such that 5^k - 4^k is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  77. Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 2, 2022.
  78. Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  79. "A007504 - OEIS". oeis.org. Retrieved June 29, 2026.
  80. Sloane, N. J. A. (ed.). "Sequence A045943". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 2, 2022.
  81. 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.
  82. 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 June 2, 2022.
  83. Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 2, 2022.
  84. 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. Retrieved June 2, 2022.
  85. Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  86. Sloane, N. J. A. (ed.). "Sequence A001792". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  87. Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  88. Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  89. Sloane, N. J. A. (ed.). "Sequence A000179 (Ménage numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 11, 2016.
  90. "A053701 - OEIS". oeis.org. Retrieved June 29, 2026.
  91. Sloane, N. J. A. (ed.). "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 2, 2022.
  92. Sloane, N. J. A. (ed.). "Sequence A094133 (Leyland prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  93. 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. Retrieved June 11, 2016.
  94. "A000124 - OEIS". oeis.org. Retrieved June 29, 2026.