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500 (number)

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For other uses, see 500 (disambiguation).
Look up five hundred in Wiktionary, the free dictionary.

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

← 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

Mathematical properties

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500 = 22 × 53. It is an Achilles number 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

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Five hundred is also

Slang names

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

Integers from 501 to 599

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500s

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501

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Main article: 501 (number)

501 = 3 × 167. It is:

  • the sum of the first 18 primes (a term of the sequence OEIS: A007504).
  • palindromic in bases 9 (6169) and 20 (15120).

502

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  • 502 = 2 × 251
  • vertically symmetric number (sequence A053701 in the OEIS)

503

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503 is:

504

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504 = 23 × 32 × 7. It is:

  is prime[12]

505

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506

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506 = 2 × 11 × 23. It is:

  is a prime number. Its decimal expansion is 252 nines, an eight, and 253 more nines.

507

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  • 507 = 3 × 132 = 232 - 23 + 1, which makes it a central polygonal number[17]
    • The age Ming had before dying.

508

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  • 508 = 22 × 127, sum of four consecutive primes (113 + 127 + 131 + 137), number of graphical forest partitions of 30,[18] since 508 = 222 + 22 + 2 it is the maximum number of regions into which 23 intersecting circles divide the plane.[19]

509

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509 is:

510s

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510

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510 = 2 × 3 × 5 × 17. 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).
  • the sum of twelve consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67).
  • a nontotient.
  • a sparsely totient number.[21]
  • a Harshad number.
  • the number of nonempty proper subsets of an 9-element set.[22]

511

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Main article: 511 (number)

511 = 7 × 73. It is:

512

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Main article: 512 (number)

512 = 83 = 29. It is:

513

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513 = 33 × 19. It is:

514

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514 = 2 × 257, it is:

515

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515 = 5 × 103, it is:

  • the sum of nine consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
  • the number of complete compositions of 11.[27]

516

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516 = 22 × 3 × 43, it is:

517

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517 = 11 × 47, it is:

  • the sum of five consecutive primes (97 + 101 + 103 + 107 + 109).
  • a Smith number.[29]

518

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518 = 2 × 7 × 37, it is:

  • = 51 + 12 + 83 (a property shared with 175 and 598).
  • a sphenic number.
  • a nontotient.
  • an untouchable number.[28]
  • palindromic and a repdigit in bases 6 (22226) and 36 (EE36).
  • a Harshad number.

519

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519 = 3 × 173, it is:

  • the sum of three consecutive primes (167 + 173 + 179)
  • palindromic in bases 9 (6369) and 12 (37312)
  • a D-number.[30]

520s

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520

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520 = 23 × 5 × 13. It is:

521

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521 is:

  • a Lucas prime.[31]
  • A Mersenne exponent, i.e. 2521−1 is prime.
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • palindromic in bases 11 (43411) and 20 (16120).

4521 - 3521 is prime

522

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522 = 2 × 32 × 29. It is:

  • the sum of six consecutive primes (73 + 79 + 83 + 89 + 97 + 101).
  • a repdigit in bases 28 (II28) and 57 (9957).
  • a Harshad number.
  • number of series-parallel networks with 8 unlabeled edges.[33]

523

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523 is:

  • a prime number.
  • the sum of seven consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89).
  • palindromic in bases 13 (31313) and 18 (1B118).
  • a prime with a prime number of prime digits[34]
  • the smallest prime number that starts a prime gap of length greater than 14

524

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524 = 22 × 131

  • number of partitions of 44 into powers of 2[35]

525

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525 = 3 × 52 × 7. It is palindromic in base ten, as well as the fifty-fifth self number greater than 1 in decimal.[36] It is also:

525 is the number of scan lines in the NTSC television standard.

526

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526 = 2 × 263, centered pentagonal number,[39] nontotient, Smith number[29]

527

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527 = 17 × 31. It is:

  • palindromic in base 15 (25215)
  • number of diagonals in a 34-gon[40]
  • also, the section of the US Tax Code regulating soft money political campaigning (see 527 groups)

528

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528 = 24 × 3 × 11. It is:

529

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529 = 232. It is:

530s

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530

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530 = 2 × 5 × 53. It is:

531

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531 = 32 × 59. It is:

  • palindromic in base 12 (38312).
  • a Harshad number.
  • number of symmetric matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to 6[42]

532

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532 = 22 × 7 × 19. It is:

533

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533 = 13 × 41. It is:

  • the sum of three consecutive primes (173 + 179 + 181).
  • the sum of five consecutive primes (101 + 103 + 107 + 109 + 113).
  • palindromic in base 19 (19119).
  • generalized octagonal number.[44]

534

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534 = 2 × 3 × 89. It is:

  • a sphenic number.
  • the sum of four consecutive primes (127 + 131 + 137 + 139).
  • a nontotient.
  • palindromic in bases 5 (41145) and 14 (2A214).
  • an admirable number.
  is prime[12]

535

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535 = 5 × 107. It is:

  for  ; this polynomial plays an essential role in Apéry's proof that   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.[45]

536

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536 = 23 × 67. It is:

  • the number of ways to arrange the pieces of the ostomachion into a square, not counting rotation or reflection.
  • the number of 1's in all partitions of 23 into odd parts[46]
  • a refactorable number.[11]
  • the lowest happy number beginning with the digit 5.

537

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537 = 3 × 179, Mertens function (537) = 0, Blum integer, D-number[30]

538

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538 = 2 × 269. It is:

539

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539 = 72 × 11

  is prime[12]

540s

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540

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540 = 22 × 33 × 5. It is:

541

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541 is:

For the Mertens function,  

542

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542 = 2 × 271. It is:

543

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543 = 3 × 181; palindromic in bases 11 (45411) and 12 (39312), D-number.[30]

  is prime[12]

544

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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. OEIS: A331452

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

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545 = 5 × 109. It is:

546

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546 = 2 × 3 × 7 × 13. It is:

  • the sum of eight consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).
  • palindromic in bases 4 (202024), 9 (6669), and 16 (22216).
  • a repdigit in bases 9 and 16.
  • 546! − 1 is prime.

547

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547 is:

548

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548 = 22 × 137. It is:

Also, every positive integer is the sum of at most 548 ninth powers;

549

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549 = 32 × 61, it is:

  • a repdigit in bases 13 (33313) and 60 (9960).
  • φ(549) = φ(σ(549)).[59]

550s

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550

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550 = 2 × 52 × 11. It is:

551

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551 = 19 × 29. It is:

  • It is the number of mathematical trees on 12 unlabeled nodes.[62]
  • the sum of three consecutive primes (179 + 181 + 191).
  • palindromic in base 22 (13122).
  • the SMTP status code meaning user is not local

552

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552 = 23 × 3 × 23. It is:

  • the number of prime knots with 11 crossings.[63]
  • the sum of six consecutive primes (79 + 83 + 89 + 97 + 101 + 103).
  • the sum of ten consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73).
  • a pronic number.[16]
  • an untouchable number.[28]
  • palindromic in base 19 (1A119).
  • a Harshad number.
  • the model number of U-552.
  • the SMTP status code meaning requested action aborted because the mailbox is full.

553

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553 = 7 × 79. It is:

  • the sum of nine consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
  • a central polygonal number.[17]
  • the model number of U-553.
  • the SMTP status code meaning requested action aborted because of faulty mailbox name.

554

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554 = 2 × 277. It is:

  • a nontotient.
  • a 2-Knödel number
  • the SMTP status code meaning transaction failed.

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

555

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Main article: 555 (number)

555 = 3 × 5 × 37 is:

  • a sphenic number.
  • palindromic in bases 9 (6769), 10 (55510), and 12 (3A312).
  • a repdigit in bases 10 and 36.
  • a Harshad number.
  • φ(555) = φ(σ(555)).[59]

556

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556 = 22 × 139. It is:

  • the sum of four consecutive primes (131 + 137 + 139 + 149).
  • an untouchable number, because it is never the sum of the proper divisors of any integer.[28]
  • a happy number.
  • the model number of U-556; 5.56×45mm NATO cartridge.

557

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557 is:

  • a prime number.
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • the number of parallelogram polyominoes with 9 cells.[64]

558

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558 = 2 × 32 × 31. It is:

  • a nontotient.
  • a repdigit in bases 30 (II30) and 61 (9961).
  • a Harshad number.
  • The sum of the largest prime factors of the first 558 is itself divisible by 558 (the previous such number is 62, the next is 993).
  • in the title of the Star Trek: Deep Space Nine episode "The Siege of AR-558"

559

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559 = 13 × 43. It is:

  • the sum of five consecutive primes (103 + 107 + 109 + 113 + 127).
  • the sum of seven consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97).
  • a nonagonal number.[65]
  • a centered cube number.[66]
  • palindromic in base 18 (1D118).
  • the model number of U-559.

560s

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560

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560 = 24 × 5 × 7. It is:

  • a tetrahedral number.[67]
  • a refactorable number.
  • palindromic in bases 3 (2022023) and 6 (23326).
  • the number of diagonals in a 35-gon[40]

561

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561 = 3 × 11 × 17. It is:

562

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562 = 2 × 281. It is:

  • a Smith number.[29]
  • an untouchable number.[28]
  • the sum of twelve consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71).
  • palindromic in bases 4 (203024), 13 (34313), 14 (2C214), 16 (23216), and 17 (1G117).
  • a lazy caterer number (sequence A000124 in the OEIS).
  • the number of Native American (including Alaskan) Nations, or "Tribes," recognized by the USA government.

56264 + 1 is prime

563

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563 is:

564

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564 = 22 × 3 × 47. It is:

  • the sum of a twin prime (281 + 283).
  • a refactorable number.
  • palindromic in bases 5 (42245) and 9 (6869).
  • number of primes <= 212.[74]

565

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565 = 5 × 113. It is:

  • the sum of three consecutive primes (181 + 191 + 193).
  • a member of the Mian–Chowla sequence.[75]
  • a happy number.
  • palindromic in bases 10 (56510) and 11 (47411).

566

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566 = 2 × 283. It is:

567

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567 = 34 × 7. It is:

  • palindromic in base 12 (3B312).
  is prime[12]

568

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568 = 23 × 71. It is:

  • the sum of the first nineteen primes (a term of the sequence OEIS: A007504).
  • a refactorable number.
  • palindromic in bases 7 (14417) and 21 (16121).
  • the smallest number whose seventh power is the sum of 7 seventh powers.
  • the room number booked by Benjamin Braddock in the 1967 film The Graduate.
  • the number of millilitres in an imperial pint.
  • the name of the Student Union bar at Imperial College London

569

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569 is:

  • a prime number.
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • a strictly non-palindromic number.[72]

570s

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570

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570 = 2 × 3 × 5 × 19. It is:

  • a triangular matchstick number[76]
  • a balanced number[77]

571

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571 is:

  • a prime number.
  • a Chen prime.
  • a centered triangular number.[26]
  • the model number of U-571 which appeared in the 2000 movie U-571

572

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572 = 22 × 11 × 13. It is:

573

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573 = 3 × 191. It is:

574

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574 = 2 × 7 × 41. It is:

  • a sphenic number.
  • a nontotient.
  • palindromic in base 9 (7079).
  • number of partitions of 27 that do not contain 1 as a part.[78]
  • number of amino acid residues in a hemoglobin molecule.

575

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575 = 52 × 23. It is:

And the sum of the squares of the first 575 primes is divisible by 575.[80]

576

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576 = 26 × 32 = 242. It is:

  • the sum of four consecutive primes (137 + 139 + 149 + 151).
  • a highly totient number.[81]
  • a Smith number.[29]
  • an untouchable number.[28]
  • palindromic in bases 11 (48411), 14 (2D214), and 23 (12123).
  • a Harshad number.
  • four-dozen sets of a dozen, which makes it 4 gross.
  • a cake number.
  • the number of parts in all compositions of 8.[82]

577

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577 is:

578

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578 = 2 × 172. It is:

  • a nontotient.
  • palindromic in base 16 (24216).
  • area of a square with diagonal 34[84]

579

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579 = 3 × 193; it is a ménage number,[85] and a semiprime.

580s

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580

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580 = 22 × 5 × 29. It is:

  • the sum of six consecutive primes (83 + 89 + 97 + 101 + 103 + 107).
  • palindromic in bases 12 (40412) and 17 (20217).

581

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581 = 7 × 83. It is:

  • the sum of three consecutive primes (191 + 193 + 197).
  • a Blum integer

582

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582 = 2 × 3 × 97. It is:

  • a sphenic number.
  • the sum of eight consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89).
  • a nontotient.
  • a vertically symmetric number (sequence A053701 in the OEIS).
  • an admirable number.

583

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583 = 11 × 53. It is:

  • palindromic in base 9 (7179).
  • number of compositions of 11 whose run-lengths are either weakly increasing or weakly decreasing[86]

584

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584 = 23 × 73. It is:

  • an untouchable number.[28]
  • the sum of totient function for first 43 integers.
  • a refactorable number.

585

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585 = 32 × 5 × 13. It is:

  • palindromic in bases 2 (10010010012), 8 (11118), and 10 (58510).
  • a repdigit in bases 8, 38, 44, and 64.
  • 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

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See also: 586 (disambiguation)

586 = 2 × 293.

587

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587 is:

  • a prime number.
  • safe prime.[3]
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • the sum of five consecutive primes (107 + 109 + 113 + 127 + 131).
  • palindromic in bases 11 (49411) and 15 (29215).
  • the outgoing port for email message submission.
  • a prime index prime.

588

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588 = 22 × 3 × 72. It is:

  • a Smith number.[29]
  • palindromic in base 13 (36313).
  • a Harshad number.

589

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589 = 19 × 31. It is:

590s

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590

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590 = 2 × 5 × 59. It is:

591

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591 = 3 × 197, D-number[30]

592

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592 = 24 × 37. It is:

  • palindromic in bases 9 (7279) and 12 (41412).
  • a Harshad number.

59264 + 1 is prime

593

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593 is:

  • a prime number.
  • a Sophie Germain prime.
  • the sum of seven consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101).
  • the sum of nine consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83).
  • an Eisenstein prime with no imaginary part.
  • a balanced prime.[71]
  • a Leyland prime[87] using 2 & 9 (29 + 92)
  • a member of the Mian–Chowla sequence.[75]
  • a strictly non-palindromic number.[72]

594

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594 = 2 × 33 × 11. It is:

  • the sum of ten consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79).
  • a nontotient.
  • palindromic in bases 5 (43345) and 16 (25216).
  • a Harshad number.
  • the number of diagonals in a 36-gon.[40]
  • a balanced number.[77]

595

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595 = 5 × 7 × 17. It is:

596

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596 = 22 × 149. It is:

  • the sum of four consecutive primes (139 + 149 + 151 + 157).
  • a nontotient.
  • a lazy caterer number (sequence A000124 in the OEIS).

597

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597 = 3 × 199. It is:

598

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598 = 2 × 13 × 23 = 51 + 92 + 83. It is:

599

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599 is:

  • a prime number.
  • a Chen prime.
  • an Eisenstein prime with no imaginary part.
  • a prime index prime.

4599 - 3599 is prime.

References

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  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. ^ a b c Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  4. ^ that is, a term of the sequence OEIS: A034961
  5. ^ that is, the first term of the sequence OEIS: A133525
  6. ^ since 503+2 is a product of two primes, 5 and 101
  7. ^ since it is a prime which is congruent to 2 modulo 3.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A001606 (Indices of prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A259180 (Amicable pairs.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-22.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A000073 (Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  11. ^ a b c Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  12. ^ a b c d e 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.
  13. ^ Wohlfahrt, K. (1985). "Macbeath's curve and the modular group". Glasgow Math. J. 27: 239–247. doi:10.1017/S0017089500006212. MR 0819842.
  14. ^ a b Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  15. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  16. ^ a b Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  17. ^ a b Sloane, N. J. A. (ed.). "Sequence A002061". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ Sloane, N. J. A. (ed.). "Sequence A000070". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A014206". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  21. ^ Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  22. ^ Sloane, N. J. A. (ed.). "Sequence A000918". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A061209 (Numbers which are the cubes of their digit sum)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  25. ^ Sloane, N. J. A. (ed.). "Sequence A045575 (Leyland numbers of the second kind)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  26. ^ a b Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  27. ^ Sloane, N. J. A. (ed.). "Sequence A107429 (Number of complete compositions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  28. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  29. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  30. ^ a b c d 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 2022-05-31.
  31. ^ Sloane, N. J. A. (ed.). "Sequence A005479 (Prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  32. ^ Dr. Kirkby (May 19, 2021). "Many more twin primes below Mersenne exponents than above Mersenne exponents". Mersenne Forum.
  33. ^ 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.
  34. ^ Sloane, N. J. A. (ed.). "Sequence A348699 (Primes with a prime number of prime digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. ^ 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.
  36. ^ 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 2024-01-09.
  37. ^ 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 2024-01-09.
  38. ^ Sloane, N. J. A. (ed.). "Sequence A113907 (Dimensions of the five sporadic Lie groups.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-01-09.
  39. ^ Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  40. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000096". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-31.
  41. ^ 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 2016-06-11.
  42. ^ 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.
  43. ^ a b Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  44. ^ Sloane, N. J. A. (ed.). "Sequence A001082 (Generalized octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  45. ^ Larmer, Brook (October 26, 2011). "Where an Internet Joke Is Not Just a Joke". New York Times. Retrieved November 1, 2011.
  46. ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  47. ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  48. ^ Snorri Sturluson (1880). "Prose Edda". p. 107.
  49. ^ Snorri Sturluson (1880). "Prose Edda". p. 82.
  50. ^ Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  51. ^ Sloane, N. J. A. (ed.). "Sequence A003154 (Centered 12-gonal numbers. Also star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  52. ^ 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 2023-10-23.
  53. ^ 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 2023-10-23.
  54. ^ Sloane, N. J. A. (ed.). "Sequence A002088". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  55. ^ Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  56. ^ Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  57. ^ Sloane, N. J. A. (ed.). "Sequence A003215 (Hex (or centered hexagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  58. ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  59. ^ a b Sloane, N. J. A. (ed.). "Sequence A006872". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  60. ^ Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  61. ^ a b Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  62. ^ "Sloane's A000055: Number of trees with n unlabeled nodes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2010-11-29. Retrieved 2021-12-19.
  63. ^ Sloane, N. J. A. (ed.). "Sequence A002863 (Number of prime knots with n crossings)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  64. ^ 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.
  65. ^ Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  66. ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  67. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  68. ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  69. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 14. ISBN 978-1-84800-000-1.
  70. ^ Sloane, N. J. A. (ed.). "Sequence A007540 (Wilson primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  71. ^ a b Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  72. ^ a b c Sloane, N. J. A. (ed.). "Sequence A016038 (Strictly non-palindromic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  73. ^ 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.
  74. ^ Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  75. ^ a b Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  76. ^ Sloane, N. J. A. (ed.). "Sequence A045943". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  77. ^ a b 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.
  78. ^ 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.
  79. ^ 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 2022-06-02.
  80. ^ 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 2022-06-02.
  81. ^ Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  82. ^ Sloane, N. J. A. (ed.). "Sequence A001792". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  83. ^ Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  84. ^ Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  85. ^ Sloane, N. J. A. (ed.). "Sequence A000179 (Ménage numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  86. ^ 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 2022-06-02.
  87. ^ Sloane, N. J. A. (ed.). "Sequence A094133 (Leyland prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  88. ^ 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 2016-06-11.
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