# 64 (number)

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

63
64 (sixty-four) is the natural number following 63 and preceding 65.
63 (sixty-three) is a natural number following 62 and preceding 64.

### 65 (number)

65
64 (sixty-four) is the natural number following 63 and preceding 65.
65 (sixty-five) is the natural number following 64 and preceding 66.

### 8

eight8 (number)number 8
Sixty-four is the square of 8, the cube of 4, and the sixth power of 2.

### 2

bracetwo2 (number)
Sixty-four is the square of 8, the cube of 4, and the sixth power of 2.

### Power of two

powers of twopower of 2powers of 2
It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime.

### Dodecagonal number

Dodecagonal
It is also a dodecagonal number and a centered triangular number.
:1, 12, 33, 64, 105, 156, 217, 288, 369, 460, 561, 672, 793, 924, 1065, 1216, 1377, 1548, 1729, 1920, 2121, 2332, 2553, 2784, 3025, 3276, 3537, 3808, 4089, 4380, 4681, 4992, 5313, 5644, 5985, 6336, 6697, 7068, 7449, 7840, 8241, 8652, 9073, 9504, 9945 ...

### Self number

self prime
In base 10, no integer added up to its own digits yields 64, hence it is a self number.
: 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, 97, 108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310, 312, 323, 334, 345, 356, 367, 378, 389, 400, 411, 413, 424, 435, 446, 457, 468, 479, 490, ...

### Erdős–Woods number

Erdős–Woods conjecture
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.
:16, 22, 34, 36, 46, 56, 64, 66, 70 ….

### Natural number

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

### 4

four4 (number)
Sixty-four is the square of 8, the cube of 4, and the sixth power of 2.

### Divisor

divisibilitydividesdivisible
It is the smallest number with exactly seven divisors.

### Mersenne prime

Mersenne numberMersenne numbersMersenne primes
It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime.

### Euler's totient function

totient functionEuler totient functiontotient
64 is the sum of Euler's totient function for the first fourteen integers.

### Centered triangular number

It is also a dodecagonal number and a centered triangular number.

### Superperfect number

super-multiperfect
64 is a superperfect number—a number such that σ(σ(n)) = 2n.

### Divisor function

sum-of-divisors functionnumber of divisorssum of divisors function
64 is a superperfect number—a number such that σ(σ(n)) = 2n.

### Graham's number

the number ''g'' 1
64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑ 3,…

### Knuth's up-arrow notation

Knuth up-arrow notationKnuth's Up-arrow operators10↑↑10
64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑ 3,…

### Atomic number

proton numberZatomic numbers
*The atomic number of gadolinium, a lanthanide

GdGd 3+ contrast
*The atomic number of gadolinium, a lanthanide

### Messier object

MessierMessier CatalogueList of Messier objects

### Apparent magnitude

apparent visual magnitudemagnitudevisual magnitude

### Galaxy

galaxiesgalacticgalactic nuclei

### Constellation

constellationsEuropean constellationModern constellation

### Coma Berenices

ComComa Berenices constellationComa