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# 84

Please do not rely on any information it contains.

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, ... $3x-1$ 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

 $\mu (84)$ 0 $M(84)$ −4 $\pi (84)$ 23 $\sigma _{1}(84)$ 224 $\sigma _{0}(84)$ 12 $\phi (84)$ 24 $\Omega (84)$ 4 $\omega (84)$ 3 $\lambda (84)$ This is the Carmichael lambda function. $\lambda (84)$ This is the Liouville lambda function.

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## 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

 $-1$ 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