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# 32

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32 is the fifth power of 2.

## Membership in core sequences

 Even numbers ..., 26, 28, 30, 32, 34, 36, 38, ... A005843 Composite numbers ..., 27, 28, 30, 32, 33, 34, 35, ... A002808 Powers of 2 ..., 4, 8, 16, 32, 64, 128, 256, ... A000079

## Sequences pertaining to 32

 Multiples of 32 0, 32, 64, 96, 128, 160, 192, 224, 256, 288, 320, 352, 384, ... A174312 ${\displaystyle 3x+1}$ sequence beginning at 21 21, 64, 32, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ... A033481

## Partitions of 32

There are 8349 partitions of 32. Of these, several partitions do the of the [FINISH WRITING]

## Roots and powers of 32

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

 ${\displaystyle {\sqrt {32}}}$ 5.65685424 A010487 32 2 1024 ${\displaystyle {\sqrt[{3}]{32}}}$ 3.17480210 A010603 32 3 32768 ${\displaystyle {\sqrt[{4}]{32}}}$ 2.37841423 A011027 32 4 1048576 ${\displaystyle {\sqrt[{5}]{32}}}$ 2.00000000 32 5 33554432 ${\displaystyle {\sqrt[{6}]{32}}}$ 1.78179743 32 6 1073741824 ${\displaystyle {\sqrt[{7}]{32}}}$ 1.64067071 32 7 34359738368 ${\displaystyle {\sqrt[{8}]{32}}}$ 1.54221082 32 8 1099511627776 ${\displaystyle {\sqrt[{9}]{32}}}$ 1.46973449 32 9 35184372088832 ${\displaystyle {\sqrt[{10}]{32}}}$ 1.41421356 A002193 32 10 1125899906842624 A009976

## Logarithms and 32nd powers

In the OEIS specifically and mathematics in general, ${\displaystyle \log x}$ refers to the natural logarithm of ${\displaystyle x}$, whereas all other bases are specified with a subscript.

As above, irrational numbers in the following table are truncated to eight decimal places.

 ${\displaystyle \log _{32}2}$ 0.2 ${\displaystyle \log _{2}32}$ A102525 2 32 4294967296 ${\displaystyle \log _{32}e}$ 0.288539 A131920* ${\displaystyle \log 32}$ 3.46573590 A016655 ${\displaystyle e^{32}}$ 7.89629601... × 10 13 ${\displaystyle \log _{32}3}$ 0.316993 A020861* ${\displaystyle \log _{3}32}$ 3.15464876 A152747** 3 32 1853020188851841 ${\displaystyle \log _{32}\pi }$ 3.02756 ${\displaystyle \log _{\pi }32}$ 0.33029922 ${\displaystyle \pi ^{32}}$ 8.10580078... × 10 15 ${\displaystyle \log _{32}4}$ 0.4 ${\displaystyle \log _{4}32}$ 2.50000000 4 32 18446744073709551616 ${\displaystyle \log _{32}5}$ 0.464386 ${\displaystyle \log _{5}32}$ 2.15338279 A152675 5 32 23283064365386962890625 ${\displaystyle \log _{32}6}$ 0.516992 ${\displaystyle \log _{6}32}$ 1.93426403 6 32 7958661109946400884391936 ${\displaystyle \log _{32}7}$ 0.561471 ${\displaystyle \log _{7}32}$ 1.78103593 7 32 1104427674243920646305299201 ${\displaystyle \log _{32}8}$ 0.6 ${\displaystyle \log _{8}32}$ 1.66666666 A020793 8 32 79228162514264337593543950336 ${\displaystyle \log _{32}9}$ 0.633985 ${\displaystyle \log _{9}32}$ 1.57732438 9 32 3433683820292512484657849089281 ${\displaystyle \log _{32}10}$ 0.664386 ${\displaystyle \log _{10}32}$ 1.50514997 10 32 100000000000000000000000000000000

* Divided by 10.

** Multiplied by 10.

(See A001016 for the 32nd powers of integers).

## Values for number theoretic functions with 32 as an argument

 ${\displaystyle \mu (32)}$ 0 ${\displaystyle M(32)}$ –4 ${\displaystyle \pi (32)}$ 11 ${\displaystyle \sigma _{1}(32)}$ 63 ${\displaystyle \sigma _{0}(32)}$ 6 ${\displaystyle \phi (32)}$ 16 ${\displaystyle \Omega (32)}$ 5 ${\displaystyle \omega (32)}$ 1 ${\displaystyle \lambda (32)}$ 8 This is the Carmichael lambda function. ${\displaystyle \lambda (32)}$ –1 This is the Liouville lambda function. ${\displaystyle \zeta (32)}$ 32! 263130836933693530167218012160000000 ${\displaystyle \Gamma (32)}$ 8222838654177922817725562880000000

## Factorization of 32 in some quadratic integer rings

In ${\displaystyle \mathbb {Z} }$, 32 has the prime factorization of 2 5. But it has different factorizations in some quadratic integer rings.

 ${\displaystyle \mathbb {Z} [i]}$ ${\displaystyle (1-i)^{5}(1+i)^{5}}$ ${\displaystyle \mathbb {Z} [{\sqrt {-2}}]}$ ${\displaystyle (-1)({\sqrt {-2}})^{10}}$ ${\displaystyle \mathbb {Z} [{\sqrt {2}}]}$ ${\displaystyle ({\sqrt {2}})^{10}}$ ${\displaystyle \mathbb {Z} [\omega ]}$ 2 5 ${\displaystyle \mathbb {Z} [{\sqrt {3}}]}$ ${\displaystyle (-1)(2-2{\sqrt {3}})(2+2{\sqrt {3}})}$ ${\displaystyle \mathbb {Z} [{\sqrt {-5}}]}$ ${\displaystyle \mathbb {Z} [\phi ]}$ 2 5 ${\displaystyle \mathbb {Z} [{\sqrt {-6}}]}$ ${\displaystyle \mathbb {Z} [{\sqrt {6}}]}$ ${\displaystyle (-1)(2-{\sqrt {6}})^{5}(2+{\sqrt {6}})^{5}}$ ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-7}})}}$ ${\displaystyle \left({\frac {1}{2}}-{\frac {\sqrt {-7}}{2}}\right)^{5}\left({\frac {1}{2}}+{\frac {\sqrt {-7}}{2}}\right)^{5}}$ ${\displaystyle \mathbb {Z} [{\sqrt {7}}]}$ ${\displaystyle (3-{\sqrt {7}})^{5}(3+{\sqrt {7}})^{5}}$ ${\displaystyle \mathbb {Z} [{\sqrt {-10}}]}$ 2 5 ${\displaystyle \mathbb {Z} [{\sqrt {10}}]}$ 2 5 ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-11}})}}$ ${\displaystyle \mathbb {Z} [{\sqrt {11}}]}$ ${\displaystyle (-1)(3-{\sqrt {11}})^{5}(3+{\sqrt {11}})^{5}}$ ${\displaystyle \mathbb {Z} [{\sqrt {-13}}]}$ ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {13}})}}$ 2 5 ${\displaystyle \mathbb {Z} [{\sqrt {-14}}]}$ ${\displaystyle \mathbb {Z} [{\sqrt {14}}]}$ ${\displaystyle (4-{\sqrt {14}})^{5}(4+{\sqrt {14}})^{5}}$ ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-15}})}}$ ${\displaystyle \mathbb {Z} [{\sqrt {15}}]}$ 2 5 ${\displaystyle \mathbb {Z} [{\sqrt {-17}}]}$ ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {17}})}}$ ${\displaystyle (-1)\left({\frac {3}{2}}-{\frac {\sqrt {17}}{2}}\right)^{5}\left({\frac {3}{2}}+{\frac {\sqrt {17}}{2}}\right)^{5}}$ ${\displaystyle {\mathcal {O}}_{\mathbb {Q} ({\sqrt {-19}})}}$ ${\displaystyle \mathbb {Z} [{\sqrt {19}}]}$ ${\displaystyle (-1)(13-3{\sqrt {19}})(13+3{\sqrt {19}})}$

REMARKS

## Representation of 32 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 100000 1012 200 112 52 44 40 35 32 2A 28 26 24 22 20 1F 1E 1D 1C

REMARKS GO HERE

## See also

 ${\displaystyle -1}$ 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