64 (number)

Last updated
63 64 65
Cardinal sixty-four
Ordinal 64th
(sixty-fourth)
Factorization 26
Divisors 1, 2, 4, 8, 16, 32, 64
Greek numeral ΞΔ´
Roman numeral LXIV, lxiv
Binary 10000002
Ternary 21013
Senary 1446
Octal 1008
Duodecimal 5412
Hexadecimal 4016

64 (sixty-four) is the natural number following 63 and preceding 65.

Contents

Mathematics

Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the seventeenth interprime, since it lies midway between the eighteenth and nineteenth prime numbers (61, 67). [1]

The aliquot sum of a power of two (2 n) is always one less than the power of two itself, therefore the aliquot sum of 64 is 63, within an aliquot sequence of two composite members (64, 63, 41, 1, 0) that are rooted in the aliquot tree of the thirteenth prime, 41. [2]

64 is:

Since it is possible to find sequences of 65 consecutive integers (intervals of length 64) such that each inner member shares a factor with either the first or the last member, 64 is the seventh Erdős–Woods number. [10]

In decimal, no integer added to the sum of its own digits yields 64; hence, 64 is the tenth self number. [11]

In four dimensions, there are 64 uniform polychora aside from two infinite families of duoprisms and antiprismatic prisms, and 64 Bravais lattices. [12]

A chessboard has 64 squares. Chess Board.svg
A chessboard has 64 squares.

See also

References

  1. Sloane, N. J. A. (ed.). "SequenceA024675(Average of two consecutive odd primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-06.
  2. Sloane, N. J. A., ed. (1975). "Aliquot sequences". The On-Line Encyclopedia of Integer Sequences . 29 (129). The OEIS Foundation: 101–107. Retrieved 2023-11-06.
  3. Sloane, N. J. A. (ed.). "SequenceA005179(Smallest number with exactly n divisors)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. Sloane, N. J. A. (ed.). "SequenceA030516(Numbers with 7 divisors. 6th powers of primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. Sloane, N. J. A. (ed.). "SequenceA019279(Superperfect numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. Sloane, N. J. A. (ed.). "SequenceA002088(Sum of totient function: a(n) is Sum_{k equal to 1..n} phi(k), cf. A000010.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-06.
  7. Sloane, N. J. A. (ed.). "SequenceA006125(a(n) equal to 2^(n*(n-1)/2).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-16.
  8. Sloane, N. J. A. (ed.). "SequenceA051624(12-gonal (or dodecagonal) numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  9. Sloane, N. J. A. (ed.). "SequenceA005448(Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  10. "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  11. "Sloane's A003052 : Self numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  12. Brown, Harold; Bülow, Rolf; Neubüser, Joachim; Wondratschek, Hans; Zassenhaus, Hans (1978), Crystallographic groups of four-dimensional space, New York: Wiley-Interscience [John Wiley & Sons], ISBN   978-0-471-03095-9, MR   0484179