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60

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Please do not rely on any information it contains.            


60 is an integer, the smallest positive integer divisible by all integers from 1 to 6 (see A003418).

Membership in core sequences

Even numbers ..., 52, 54, 56, 58, 60, 62, 64, 66, ... A005843
Composite numbers ..., 56, 57, 58, 60, 62, 63, 64, 65, ... A002808
Abundant numbers ..., 48, 54, 56, 60, 66, 70, 72, 78, ... A005101
Binary partition numbers ..., 26, 36, 46, 60, 74, 94, 114, 140, ... A000123
Number of ways of dissecting a polygon
into quadrilaterals
..., 2, 5, 16, 60, 261, 1243, 6257, ... A005036
Orders of non-cyclic simple groups 60, 168, 360, 504, 660, 1092, 2448, ... A001034

Sequences pertaining to 60

Multiples of 60 0, 60, 120, 180, 240, 300, 360, ... A169823
Divisors of 60 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 A018266

Partitions of 60

There are 966467 partitions of 60.

The Goldbach representations of 60 are: 7 + 53 = 13 + 47 = 17 + 43 = 19 + 41 = 23 + 37 = 29 + 31.

Roots and powers of 60

PLACEHOLDER

Values for number theoretic functions with 60 as an argument

PLACEHOLDER

Factorization of 60 in some quadratic integer rings

PLACEHOLDER

Representation of 60 in various bases

Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Representation 111100 2020 330 220 140 114 74 66 60 55 50 48 44 40 3C 39 36 33 30

As you can see from the table above, 60 is a Harshad number in every base from binary to vigesimal, except bases 8, 14, 18. It is also a Harshad number in bases 21, 25, 26, 28, 29, 30, 31, 41, 46, 49, 51, 55, 56, 57, 58, 59, and trivially in base 60 and above.

See also

Some integers
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
1729