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# 42

Please do not rely on any information it contains.

42 is an integer It is the fifth Catalan number, and the last one which is an integral multiple of the immediately preceding Catalan number (14, see A000108).

## Membership in core sequences

 Even numbers ..., 36, 38, 40, 42, 44, 46, 48, ... A005843 Composite numbers ..., 38, 39, 40, 42, 44, 45, 46, ... A002808 Squarefree numbers ..., 38, 39, 41, 42, 31, 33, 34, ... A005117 Oblong numbers ..., 12, 20, 30, 42, 56, 72, 90, ... A002378 Catalan numbers 1, 1, 2, 5, 14, 42, 132, 429, ... A000108 Denominators ofBernoulli numbers 1, 2, 6, 1, 30, 1, 42, 1, 30, 1, ... A027642

## Sequences pertaining to 42

 Multiples of 42 0, 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, ... Divisors of 42 1, 2, 3, 6, 7, 14, 21, 42 A018258 ${\displaystyle 3x-1}$ sequence starting at 84 84, 42, 21, 62, 31, 92, 46, 23, 68, 34, 17, 50, 25, 74, 37, 110, ... A008898

## Partitions of 42

There are 53174 partitions of 42.

The Goldbach representations of 42 are 5 + 37 = 11 + 31 = 13 + 29 = 19 + 23.

## Roots and powers of 42

In the table below, irrational numbers are given truncated to eight decimal places.

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## Representation of 42 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 101010 1120 222 132 110 60 52 46 42 39 36 33 30 2C 2A 28 26 24 22

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 ${\displaystyle -1}$ 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