This site is supported by donations to The OEIS Foundation.
60
From OeisWiki
60 is an integer, the smallest positive integer divisible by all integers from 1 to 6 (see A003418).
Contents
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
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 |