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# 132

Please do not rely on any information it contains.

132 is an integer.

## Membership in core sequences

 Even numbers ..., 126, 128, 130, 132, 134, 136, 138, ... A005843 Composite numbers ..., 128, 129, 130, 132, 133, 134, 135, ... A002808 Oblong numbers ..., 72, 90, 110, 132, 156, 182, 210, ... A002378 Catalan numbers ..., 5, 14, 42, 132, 429, 1430, 4862, ... A000108 Quarter-squares ..., 100, 110, 121, 132, 144, 156, 169, ... A002620

## Sequences pertaining to 132

 Multiples of 132 0, 132, 264, 396, 528, 660, 792, 924, 1056, 1188, 1320, 1452, 1584, ... ${\displaystyle 7x+1}$ sequence beginning at 11 11, 76, 38, 19, 132, 66, 33, 230, 115, 804, 402, 201, 1406, 703, 4920, ... A287330

## Partitions of 132

There are 6620830889 partitions of 132.

The Goldbach representations of 132 are: 127 + 5 = 113 + 19 = 109 + 23 = 103 + 29 = 101 + 31 = 89 + 43 = 79 + 53 = 73 + 59 = 71 + 61 = 132.

## Roots and powers of 132

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

TABLE GOES HERE

## Values for number theoretic functions with 132 as an argument

 ${\displaystyle \mu (132)}$ 0 ${\displaystyle M(132)}$ −3 ${\displaystyle \pi (132)}$ 32 ${\displaystyle \sigma _{1}(132)}$ 336 ${\displaystyle \sigma _{0}(132)}$ 12 ${\displaystyle \phi (132)}$ 40 ${\displaystyle \Omega (132)}$ 4 ${\displaystyle \omega (132)}$ 2 ${\displaystyle \lambda (132)}$ 10 This is the Carmichael lambda function. ${\displaystyle \lambda (132)}$ 1 This is the Liouville lambda function.

## Factorization of 132 in some quadratic integer rings

In ${\displaystyle \mathbb {Z} }$, 132 has the prime factorization of 2 2 × 3 × 11. But it has different factorizations in some quadratic integer rings.

TABLE GOES HERE

## Representation of 132 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 10000100 11220 2010 1012 340 246 204 156 132 110 B0 A2 96 8C 84 7D 76 6I 6C

Notice that 132 is the smallest number which is the sum of all of the 2-digit numbers that can be formed with its base 10 digits: 13 + 12 + 31 + 32 + 21 + 23 = 132.

 ${\displaystyle -1}$ 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