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# 144

Please do not rely on any information it contains.

144 is an integer, the square of 12.

## Membership in core sequences

 Even numbers ..., 138, 140, 142, 144, 146, 148, 150, ... A005843 Composite numbers ..., 8, 9, 10, 144, 145, 146, 147, 148, ... A002808 Abundant numbers ..., 132, 138, 140, 144, 150, 156, 160, ... A005101 Fibonacci numbers ..., 34, 55, 89, 144, 233, 377, 610, ... A000045 Perfect squares ..., 81, 100, 121, 144, 169, 196, 225, ... A000290 Loeschian numbers ..., 129, 133, 139, 144, 147, 148, 151, ... A003136

Note that 144 is both a perfect square and a Fibonacci number. In fact, 144 is the largest perfect power to also be a Fibonacci number (see A227875).

## Sequences pertaining to 144

 Divisors of 144 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 A018302 Multiples of 144 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, ... A008594

## Partitions of 144

There are 22540654445 partitions of 144.

The Goldbach representations of 144 are 139 + 5 = 137 + 7 = 131 + 13 = 127 + 17 = 113 + 31 = 107 + 37 = 103 + 41 = 101 + 43 = 97 + 47 = 83 + 61 = 73 + 71 = 144.

## Roots and powers of 144

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

 ${\displaystyle {\sqrt {144}}}$ 12 A130706 144 2 20736 ${\displaystyle {\sqrt[{3}]{144}}}$ 5.24148 144 3 2985984 ${\displaystyle {\sqrt[{4}]{144}}}$ 3.4641 A010469 144 4 429981696 ${\displaystyle {\sqrt[{5}]{144}}}$ 2.70192 144 5 61917364224 ${\displaystyle {\sqrt[{6}]{144}}}$ 2.28943 A010584 144 6 8916100448256 ${\displaystyle {\sqrt[{7}]{144}}}$ 2.03394 144 7 1283918464548864 ${\displaystyle {\sqrt[{8}]{144}}}$ 1.86121 A011009 144 8 184884258895036416 ${\displaystyle {\sqrt[{9}]{144}}}$ 1.73707 144 9 26623333280885243904 ${\displaystyle {\sqrt[{10}]{144}}}$ 1.64375 A011097 144 10 3833759992447475122176 ${\displaystyle {\sqrt[{11}]{144}}}$ 1.57114 144 11 552061438912436417593344 ${\displaystyle {\sqrt[{12}]{144}}}$ 1.51309 A011305 144 12 79496847203390844133441536

## Values for number theoretic functions with 144 as an argument

 ${\displaystyle \mu (144)}$ 0 ${\displaystyle M(144)}$ −1 ${\displaystyle \pi (144)}$ 34 ${\displaystyle \sigma _{1}(144)}$ 403 ${\displaystyle \sigma _{0}(144)}$ 15 ${\displaystyle \phi (144)}$ 48 ${\displaystyle \Omega (144)}$ 6 ${\displaystyle \omega (144)}$ 2 ${\displaystyle \lambda (144)}$ This is the Carmichael lambda function. ${\displaystyle \lambda (144)}$ This is the Liouville lambda function.

## Factorization of 144 in some quadratic integer rings

As was mentioned above, 144 is the product of 2 4 and 3 2. But it has different factorizations in some quadratic integer rings.

PLACEHOLDER

## Representation of 144 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 10010000 12100 2100 1034 400 264 220 170 144 121 100 B1 A4 99 90 88 80 7B 74

144 is a Harshad number in every base from 2 through 19 except base 14.

 ${\displaystyle -1}$ 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