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42

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This article is under construction.            

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 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
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.

TABLE GOES HERE

Logarithms and 42nd powers

REMARKS

TABLE

Values for number theoretic functions with 42 as an argument

TABLE GOES HERE

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

REMARKS

TABLE GOES HERE

REMARKS

Factorization of 42 in some quadratic integer rings

PLACEHOLDER

TABLE GOES HERE

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

REMARKS GO HERE

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