64 (number)

Last updated
63 64 65
Cardinal sixty-four
Ordinal 64th
(sixty-fourth)
Factorization 26
Divisors 1, 2, 4, 8, 16, 32, 64
Greek numeral ΞΔ´
Roman numeral LXIV
Binary 10000002
Ternary 21013
Senary 1446
Octal 1008
Duodecimal 5412
Hexadecimal 4016

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

Contents

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 thirtenth prime, 41. [2]

64 is:

64 is the fourth superperfect number — a number such that σ(σ(n)) = 2n. [3]

64 is the sum of Euler's totient function for the first fourteen integers. [4]

The number of graphs on four labeled nodes is 64. [5]

It is also the fourth dodecagonal number, [6] and seventh centered triangular number. [7]

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. [8]

In decimal, no integer added to the sum of its own digits yields 64; hence, 64 is the tenth self number. [9]

64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑3↑↑↑↑3 3, …

There are 64 total vertices in a 6-cube.

In the fourth dimension, there are 64 uniform polychora aside from two infinite families of duoprisms and antiprismatic prisms, and 64 Bravais lattices. [10]

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. Chess Board.svg
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.

I Ching

The number of hexagrams in the I Ching (that is also the maximum number of strokes in any Chinese character).

See also

Related Research Articles

76 (seventy-six) is the natural number following 75 and preceding 77.

86 (eighty-six) is the natural number following 85 and preceding 87.

34 (thirty-four) is the natural number following 33 and preceding 35.

46 (forty-six) is the natural number following 45 and preceding 47.

58 (fifty-eight) is the natural number following 57 and preceding 59.

91 (ninety-one) is the natural number following 90 and preceding 92.

100 or one hundred is the natural number following 99 and preceding 101.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

400 is the natural number following 399 and preceding 401.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

2000 is a natural number following 1999 and preceding 2001.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

135 is the natural number following 134 and preceding 136.

100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.

240 is the natural number following 239 and preceding 241.

744 is the natural number following 743 and preceding 745.

888 is the natural number following 887 and preceding 889.

References

  1. Sloane, N. J. A. (ed.). "SequenceA024675(Average of two consecutive odd primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-06.
  2. Sloane, N. J. A., ed. (1975). "Aliquot sequences". The On-Line Encyclopedia of Integer Sequences . The OEIS Foundation. 29 (129): 101–107. Retrieved 2023-11-06.
  3. "Sloane's A019279 : Superperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  4. Sloane, N. J. A. (ed.). "SequenceA002088(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.
  5. Sloane, N. J. A. (ed.). "SequenceA006125(a(n) equal to 2^(n*(n-1)/2).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-16.
  6. "Sloane's A051624 : 12-gonal (or dodecagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  7. "Sloane's A005448 : Centered triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  8. "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  9. "Sloane's A003052 : Self numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  10. 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