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# 126

Please do not rely on any information it contains.

126 is an integer.

## Membership in core sequences

 Even numbers ..., 120, 122, 124, 126, 128, 130, 132, ... A005843 Composite numbers ..., 123, 124, 125, 126, 128, 129, 130, ... A002808 Abundant numbers ..., 112, 114, 120, 126, 132, 138, ... A005101

In Pascal's triangle, 126 occurs four times, the first two times in row 9 as the sum of 56 and 70 from row 8.

## Sequences pertaining to 126

 Multiples of 126 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, 1386, 1512, ... Divisors of 126 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 A018295

## Partitions of 126

There are 3519222692 partitions of 126.

The Goldbach representations of 126 are: 113 + 13 = 109 + 17 = 107 + 19 = 103 + 23 = 97 + 29 = 89 + 37 = 83 + 43 = 79 + 47 = 73 + 53 = 67 + 59 = 126.

## Roots and powers of 126

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

TABLE GOES HERE

## Values for number theoretic functions with 126 as an argument

 ${\displaystyle \mu (126)}$ 0 ${\displaystyle M(126)}$ −1 ${\displaystyle \pi (126)}$ 30 ${\displaystyle \sigma _{1}(126)}$ ${\displaystyle \sigma _{0}(126)}$ ${\displaystyle \phi (126)}$ ${\displaystyle \Omega (126)}$ 4 ${\displaystyle \omega (126)}$ 3 ${\displaystyle \lambda (126)}$ This is the Carmichael lambda function. ${\displaystyle \lambda (126)}$ This is the Liouville lambda function.

REMARKS

TABLE

## Representation of 126 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 1111110 11200 1332 1001 330 240 176 150 126 105 A6 99 90 86 7E 77 70 6C 66

 ${\displaystyle -1}$ 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