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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.

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

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

References