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From Wikipedia, the free encyclopedia

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

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Transcription

Contents

In mathematics

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

In astronomy

In technology

In other fields

A chessboard has 64 squares
A chessboard has 64 squares

Sixty-four is:

See also

References

  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.
This page was last edited on 21 August 2019, at 09:08
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