"Sixty-four" redirects here. For other uses, see
64 .
Natural number
64 (sixty-four ) is the natural number following 63 and preceding 65 .
Mathematics [ edit ]
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:
the smallest number with exactly seven divisors ,[3]
the first whole number (greater than one) that is both a perfect square, and a perfect cube,[4]
the lowest positive power of two that is not adjacent to either a Mersenne prime or a Fermat prime ,
the fourth superperfect number — a number such that σ (σ(n )) = 2n ,[5]
the sum of Euler's totient function for the first fourteen integers,[6]
the number of graphs on four labeled nodes,[7]
the index of Graham's number in the rapidly growing sequence 3↑↑↑↑ 3, 3 ↑3↑↑↑↑3 3, …
the number of vertices in a 6-cube ,
the fourth dodecagonal number ,[8]
and the seventh centered triangular number .[9]
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]
In other fields [ edit ]
Science [ edit ]
64 is the atomic number of gadolinium , a lanthanide .
64 is the number of codons in the RNA codon table of the genetic code .
64 is the size in bits of certain data types in some computer programming languages , where a 64-bit integer can represent values up to 264 = 18,446,744,073,709,551,616.
A chessboard has 64 squares.
64 is the number of squares in a regular eight by eight chessboard .
64 is the maximum item stack size in Minecraft , where the number is called a 'stack'.
The 1996 Nintendo console is also called the Nintendo 64.
I Ching [ edit ]
The number of hexagrams in the I Ching (that is also the maximum number of strokes in any Chinese character ).
Song When I'm Sixty-Four by The Beatles
See also [ edit ]
References [ edit ]
^ Sloane, N. J. A. (ed.). "Sequence A024675 (Average of two consecutive odd primes.)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-06 .
^ 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 .
^ Sloane, N. J. A. (ed.). "Sequence A005179 (Smallest number with exactly n divisors)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A030516 (Numbers with 7 divisors. 6th powers of primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A019279 (Superperfect numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002088 (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 .
^ Sloane, N. J. A. (ed.). "Sequence A006125 (a(n) equal to 2^(n*(n-1)/2).)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-16 .
^ Sloane, N. J. A. (ed.). "Sequence A051624 (12-gonal (or dodecagonal) numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A059756 : Erdős-Woods numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30 .
^ "Sloane's A003052 : Self numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-30 .
^ 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
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