64 (number)

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← 63 64 65 →
Cardinal sixty-four
Ordinal 64th
(sixty-fourth)
Factorization 26
Divisors 1, 2, 4, 8, 16, 32, 64
Roman numeral LXIV
Binary 10000002
Ternary 21013
Quaternary 10004
Quinary 2245
Senary 1446
Octal 1008
Duodecimal 5412
Hexadecimal 4016
Vigesimal 3420
Base 36 1S36

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]

Astronomy[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.