38

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38 is an integer.

Membership in core sequences

Even numbers	..., 32, 34, 36, 38, 40, 42, 44, ...	A005843
Squarefree numbers	..., 34, 35, 37, 38, 39, 41, 42, ...	A005117

Sequences pertaining to 38

Multiples of 38	0, 38, 76, 114, 152, 190, 228, 266, 304, 342, 380, 418, 456, ...
$3x+1$ sequence starting at 33	33, 100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, ...	A008880

Partitions of 38

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Roots and powers of 38

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

${\sqrt {38}}$	6.16441400	A010492	38 2	1444
${\sqrt[{3}]{38}}$	3.36197540	A010609	38 3	54872
${\sqrt[{4}]{38}}$	2.48282379	A011032	38 4	2085136
${\sqrt[{5}]{38}}$	2.06993505	A011123	38 5	79235168
${\sqrt[{6}]{38}}$	1.83356903		38 6	3010936384
${\sqrt[{7}]{38}}$	1.68144772		38 7	114415582592
${\sqrt[{8}]{38}}$	1.57569787		38 8	4347792138496
${\sqrt[{9}]{38}}$	1.49806794		38 9	165216101262848
${\sqrt[{10}]{38}}$	1.43872688		38 10	6278211847988224
				A009982

Logarithms and 38th powers

REMARKS

TABLE

Values for number theoretic functions with 38 as an argument

$\mu (38)$	1
$M(38)$	−1
$\pi (38)$	11
$\sigma _{1}(38)$	60
$\sigma _{0}(38)$	4
$\phi (38)$	18
$\Omega (38)$	2
$\omega (38)$	2
$\lambda (38)$	18	This is the Carmichael lambda function.
$\lambda (38)$	1	This is the Liouville lambda function.
$\zeta (38)$
38!	523022617466601111760007224100074291200000000
$\Gamma (38)$	13763753091226345046315979581580902400000000

Factorization of some small integers in a quadratic integer ring adjoining the square roots of −38, 38

The commutative quadratic integer ring with unity $\mathbb {Z} [{\sqrt {38}}]$, with units of the form $\pm (37+6{\sqrt {38}})^{n}\,$ ($n\in \mathbb {Z}$), is a unique factorization domain.

$n$	$\mathbb {Z} [{\sqrt {38}}]$
2	$(-1)(6-{\sqrt {38}})(6+{\sqrt {38}})$
3	Prime
4	$(6-{\sqrt {38}})^{2}(6+{\sqrt {38}})^{2}$
5	Prime
6	$(-1)(6-{\sqrt {38}})(6+{\sqrt {38}})3$
7	Prime
8	$(-1)(6-{\sqrt {38}})^{3}(6+{\sqrt {38}})^{3}$
9	3 2
10	$(-1)(6-{\sqrt {38}})(6+{\sqrt {38}})5$
11	$(7-{\sqrt {38}})(7+{\sqrt {38}})$
12	$(6-{\sqrt {38}})^{2}(6+{\sqrt {38}})^{2}3$
13	$(-1)(5-{\sqrt {38}})(5+{\sqrt {38}})$
14	$(-1)(6-{\sqrt {38}})(6+{\sqrt {38}})7$
15	3 × 5
16	$(6-{\sqrt {38}})^{4}(6+{\sqrt {38}})^{4}$
17	$(13-2{\sqrt {38}})(13+2{\sqrt {38}})$
18	$(-1)(6-{\sqrt {38}})(6+{\sqrt {38}})3^{2}$
19	$(19-3{\sqrt {38}})(19+3{\sqrt {38}})$
20	$(6-{\sqrt {38}})^{2}(6+{\sqrt {38}})^{2}5$

Unlike $\mathbb {Z} [{\sqrt {38}}]$, $\mathbb {Z} [{\sqrt {-38}}]$ is not a unique factorization domain at all, having class number 6. But the window of 2 through 21 does not provide as interesting a window for the of the [FINISH WRITING]

Factorization of 38 in some quadratic integer rings

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TABLE GOES HERE

Representation of 38 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	100110	1102	212	123	102	53	46	42	38	35	32	2C	2A	28	26	24	22	20	1I

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