"Sixty-four" redirects here. For other uses, see
64 .
Natural number
64 (sixty-four ) is the
natural number following
63 and preceding
65 .
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:
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
Science
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.
Gaming
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
The number of
hexagrams in the
I Ching (that is also the maximum number of
strokes in any
Chinese character ).
Media
Song
When I'm Sixty-Four by
The Beatles
See also
References
^
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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10,000,000
100,000,000
1,000,000,000