"Sixty-four" redirects here. For other uses, see
64 .
Natural number
64 (sixty-four ) is thenatural number following63 and preceding65 .
Sixty-four is the square of8 , the cube of4 , and thesixth power of2 . It is the seventeenthinterprime , since it lies midway between the eighteenth and nineteenth prime numbers (61 ,67 ).[ 1]
Thealiquot sum of a power of two (2 n 63 , within analiquot 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 sevendivisors ,[ 3] the first whole number (greater than one) that is both a perfect square, and a perfect cube,[ 4] the lowest positivepower of two that is not adjacent to either aMersenne prime or aFermat prime , the fourthsuperperfect number — a number such thatσ n )) = 2n ,[ 5] the sum ofEuler's totient function for the first fourteen integers,[ 6] the number ofgraphs on four labeled nodes,[ 7] the index ofGraham's number in the rapidly growing sequence 3↑↑↑↑ 3, 3 ↑3↑↑↑↑3 3, ... the number ofvertices in a6-cube , the fourthdodecagonal number ,[ 8] and the seventhcentered 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 seventhErdős–Woods number .[ 10]
Indecimal , no integer added to the sum of its own digits yields 64; hence, 64 is thetenth self number .[ 11]
Infour dimensions , there are 64uniform polychora aside from two infinite families ofduoprisms and antiprismatic prisms , and 64Bravais lattices .[ 12]
Achessboard has 64 squares. ^ Sloane, N. J. A. (ed.)."Sequence A024675 (Average of two consecutive odd primes.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2023-11-06 .^ Sloane, N. J. A. , ed. (1975)."Aliquot sequences" .The On-Line Encyclopedia of Integer Sequences 29 (129). TheOEIS Foundation :101– 107. Retrieved2023-11-06 .^ Sloane, N. J. A. (ed.)."Sequence A005179 (Smallest number with exactly n divisors)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A030516 (Numbers with 7 divisors. 6th powers of primes)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A019279 (Superperfect numbers)" .TheOn-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.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2023-11-06 .^ Sloane, N. J. A. (ed.)."Sequence A006125 (a(n) equal to 2^(n*(n-1)/2).)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-01-16 .^ Sloane, N. J. A. (ed.)."Sequence A051624 (12-gonal (or dodecagonal) numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A005448 (Centered triangular numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ "Sloane's A059756 : Erdős-Woods numbers" .The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2016-05-30 .^ "Sloane's A003052 : Self numbers" .The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2016-05-30 .^ 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
400 to 999
400s, 500s, and 600s 700s, 800s, and 900s
1000s and 10,000s
1000s 10,000s
100,000s to 10,000,000,000,000s
100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000
