32

This article is under construction.

Please do not rely on any information it contains.

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
$3x+1$ 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.

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

Logarithms and 32nd powers

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

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

$\log _{32}2$	0.20000000		$\log _{2}32$		A102525	2 32	4294967296
$\log _{32}e$	0.28853900	A131920*	$\log 32$	3.46573590	A016655	$e^{32}$	7.89629601... × 10 13
$\log _{32}3$	0.31699250	A020861*	$\log _{3}32$	3.15464876	A152747**	3 32	1853020188851841
$\log _{32}\pi$	3.02755780		$\log _{\pi }32$	0.33029922		$\pi ^{32}$	8.10580078... × 10 15
$\log _{32}4$	0.40000000		$\log _{4}32$	2.50000000		4 32	18446744073709551616
$\log _{32}5$	0.46438561		$\log _{5}32$	2.15338279	A152675	5 32	23283064365386962890625
$\log _{32}6$	0.51699250		$\log _{6}32$	1.93426403		6 32	7958661109946400884391936
$\log _{32}7$	0.56147098		$\log _{7}32$	1.78103593		7 32	1104427674243920646305299201
$\log _{32}8$	0.60000000		$\log _{8}32$	1.66666666	A020793	8 32	79228162514264337593543950336
$\log _{32}9$	0.63398500		$\log _{9}32$	1.57732438		9 32	3433683820292512484657849089281
$\log _{32}10$	0.66438561		$\log _{10}32$	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

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

Factorization of 32 in some quadratic integer rings

In $\mathbb {Z}$, 32 has the prime factorization of 2⁵. But it has different factorizations in some quadratic integer rings.

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

The relationship of –32, 32 to quadratic integer rings adjoining ${\sqrt {-2}}$, ${\sqrt {2}}$

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

Some integers

							$-1$
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