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84
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84 is an integer. A multiple of 14, it is also the largest order of a permutation of 14 elements.
Contents
Membership in core sequences
Even numbers | ..., 78, 80, 82, 84, 86, 88, 90, ... | A005843 |
Composite numbers | ..., 80, 81, 82, 84, 85, 86, 87, ... | A002808 |
Abundant numbers | ..., 72, 78, 80, 84, 88, 90, 96, ... | A005101 |
Tetrahedral numbers | ..., 20, 35, 56, 84, 120, 165, ... | A000292 |
Sequences pertaining to 84
Divisors of 84 | 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 | A018276 |
Multiples of 84 | 84, 168, 252, 336, 420, 504, 588, 672, 756, 840, 924, 1008, 1092, ... | |
sequence starting at 84 | 84, 42, 21, 62, 31, 92, 46, 23, 68, 34, 17, 50, 25, 74, 37, 110, 55, ... | A008898 |
Partitions of 84
There are 26543660 partitions of 84.
The Goldbach partitions are 5 + 79 = 11 + 73 = 13 + 71 = 17 + 67 = 23 + 61 = 31 + 53 = 37 + 47 = 41 + 43.
Roots and powers of 84
In the table below, irrational numbers are given truncated to eight decimal places.
TABLE GOES HERE
Values for number theoretic functions with 84 as an argument
0 | ||
−4 | ||
23 | ||
224 | ||
12 | ||
24 | ||
4 | ||
3 | ||
This is the Carmichael lambda function. | ||
This is the Liouville lambda function. |
Factorization of 84 in some quadratic integer rings
REMARKS GO HERE
TABLE GOES HERE
Representation of 84 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 84 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 1010100 | 10010 | 1110 | 314 | 220 | 150 | 124 | 103 | 84 | 77 | 70 | 66 | 60 | 59 | 54 | 4G | 4C | 48 | 44 |
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 |