64 (number)

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← 63 64 65 →
Cardinalsixty-four
Ordinal64th
(sixty-fourth)
Factorization26
Divisors1, 2, 4, 8, 16, 32, 64
Greek numeralΞΔ´
Roman numeralLXIV
Binary10000002
Ternary21013
Quaternary10004
Quinary2245
Senary1446
Octal1008
Duodecimal5412
Hexadecimal4016
Vigesimal3420
Base 361S36

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

In mathematics[edit]

Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime. 64 is the sum of Euler's totient function for the first fourteen integers. It is also a dodecagonal number[1] and a centered triangular number.[2] 64 is also the first whole number that is both a perfect square and a perfect cube.

Since it is possible to find sequences of 64 consecutive integers such that each inner member shares a factor with either the first or the last member, 64 is an Erdős–Woods number.[3]

In base 10, no integer added up to its own digits yields 64, hence it is a self number.[4]

64 is a superperfect number—a number such that σ(σ(n)) = 2n.[5]

64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑3↑↑↑↑3 3,…

In science[edit]

In astronomy[edit]

In technology[edit]

In other fields[edit]

A chessboard has 64 squares

Sixty-four is:

See also[edit]

References[edit]

  1. ^ "Sloane's A051624 : 12-gonal (or dodecagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. ^ "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  3. ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  4. ^ "Sloane's A003052 : Self numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  5. ^ "Sloane's A019279 : Superperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.