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# 46

Please do not rely on any information it contains.

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, ... ${\displaystyle 3x+1}$ sequence starting at 15 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, ... A033480 ${\displaystyle 3x-1}$ sequence starting at 84 84, 42, 21, 62, 31, 92, 46, 23, 68, 34, 17, 50, 25, 74, 37, 110, ... A008898

## Partitions of 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.

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

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PLACEHOLDER

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## 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

 ${\displaystyle -1}$ 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