42

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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 of Bernoulli 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
$3x-1$ 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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Logarithms and 42nd powers

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TABLE

Values for number theoretic functions with 42 as an argument

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Factorization of some small integers in a quadratic integer ring adjoining the square roots of −42, 42

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Factorization of 42 in some quadratic integer rings

PLACEHOLDER

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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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See also

Some integers

							$-1$
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