46

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46 is an integer. It is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9 by 9 chessboard.

Membership in core sequences

Even numbers	..., 40, 42, 44, 46, 48, 50, 52, ...	A005843
Composite numbers	..., 42, 44, 45, 46, 48, 49, 50, ...	A002808
Semiprimes	..., 35, 38, 39, 46, 49, 51, 55, ...	A001358
Squarefree numbers	..., 41, 42, 43, 46, 47, 51, 53, ...	A005117
Deficient numbers	..., 43, 44, 45, 46, 47, 49, 50, ...	A005100
Central polygonal numbers	..., 22, 29, 37, 46, 56, 67, 79, ...	A000124
Wedderburn-Etherington numbers	..., 6, 11, 23, 46, 98, 207, 451, ...	A001190

Sequences pertaining to 46

Multiples of 46	0, 46, 92, 138, 184, 230, 276, 322, 368, 414, 460, 506, 552, ...
$3x+1$ sequence starting at 15	15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, ...	A033480
$3x-1$ sequence starting at 84	84, 42, 21, 62, 31, 92, 46, 23, 68, 34, 17, 50, 25, 74, 37, 110, ...	A008898

Partitions of 46

There are 105558 partitions of 46.

The Goldbach representations of 46 are 43 + 3 = 41 + 5 = 29 + 17 = 23 + 23.

Roots and powers of 46

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

TABLE GOES HERE

Values for number theoretic functions with 46 as an argument

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Factorization of some small integers in a quadratic integer ring adjoining the square roots of −46, 46

The commutative quadratic integer ring with unity $\mathbb {Z} [{\sqrt {46}}]$, with units of the form $\pm (24335+3588{\sqrt {46}})^{n}\,$ ($n\in \mathbb {Z}$), is a unique factorization domain. By contrast, $\mathbb {Z} [{\sqrt {-46}}]$ is not a unique factorization domain.

TABLE GOES HERE

Factorization of 46 in some quadratic integer rings

PLACEHOLDER

TABLE GOES HERE

Representation of 46 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	101110	1201	232	141	114	64	56	51	46	42	3A	37	34	31	2E	2C	2A	28	26

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