163

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163 is an integer.

Membership in core sequences

Odd numbers	..., 157, 159, 161, 163, 165, 167, 169, ...	A005408
Prime numbers	..., 149, 151, 157, 163, 167, 173, 179, ...	A000040
Lucky numbers	..., 141, 151, 159, 163, 169, 171, 189, ...	A001358
Squarefree numbers	..., 158, 159, 161, 163, 165, 166, 167, ...	A005117
Loeschian numbers	..., 151, 156, 157, 163, 169, 171, 172, ...	A003136

In Pascal's triangle, 163 occurs twice.

Sequences pertaining to 163

Multiples of 163	0, 163, 326, 489, 652, 815, 978, 1141, 1304, ...
$3x+1$ sequence beginning at 163	163, 490, 245, 736, 368, 184, 92, 46, 23, 70, ...

Partitions of 163

PLACEHOLDER

Roots and powers of 163

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

$\sqrt{163}$	12.76714533	A210963	163 2	26569
$\sqrt[3]{163}$	5.46255557		163 3	4330747
$\sqrt[4]{163}$	3.57311423		163 4	705911761
$\sqrt[5]{163}$	2.76973054		163 5	115063617043
$\sqrt[6]{163}$	2.33721106		163 6	18755369578009
$\sqrt[7]{163}$	2.07026910		163 7	3057125241215467
$\sqrt[8]{163}$	1.89026829		163 8	498311414318121121
$\sqrt[9]{163}$	1.76115922		163 9	81224760533853742723
$\sqrt[10]{163}$	1.66425074		163 10	13239635967018160063849

Logarithms and 163rd powers

REMARKS

TABLE

Values for number theoretic functions with 163 as an argument

$\mu (163)$	−1
$M(163)$	0
$\pi (163)$	38
${\sigma }_1(163)$	164
${\sigma }_0(163)$	2
$\varphi (163)$	162
$\mathrm{\Omega }(163)$	1
$\omega (163)$	1
$\lambda (163)$	162	This is the Carmichael lambda function.
$\lambda (163)$	−1	This is the Liouville lambda function.

Factorization of some small integers in a quadratic integer ring adjoining $\sqrt{-163}$, $\sqrt{163}$

PLACEHOLDER

Factorization of 163 in some quadratic integer rings

As was mentioned above, 163 is prime in $\mathbb{\mathbb{Z}}$. But it has different factorizations in some quadratic integer rings.

$\mathbb{\mathbb{Z}}[i]$	Prime
$\mathbb{\mathbb{Z}}[\sqrt{-2}]$	$(1-9\sqrt{-2})(1+9\sqrt{-2})$	$\mathbb{\mathbb{Z}}[\sqrt{2}]$	Prime
$\mathbb{\mathbb{Z}}[\omega ]$	$(3-11\omega )(14+11\omega )$	$\mathbb{\mathbb{Z}}[\sqrt{3}]$
$\mathbb{\mathbb{Z}}[\sqrt{-5}]$	Irreducible	$\mathbb{\mathbb{Z}}[\varphi ]$
$\mathbb{\mathbb{Z}}[\sqrt{-6}]$		$\mathbb{\mathbb{Z}}[\sqrt{6}]$	$(53-21\sqrt{6})(53+21\sqrt{6})$
${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{-7})}$	$(10-3\sqrt{-7})(10+3\sqrt{-7})$	$\mathbb{\mathbb{Z}}[\sqrt{7}]$	Prime
$\mathbb{\mathbb{Z}}[\sqrt{-10}]$	Irreducible	$\mathbb{\mathbb{Z}}[\sqrt{10}]$	Irreducible
${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{-11})}$	$(8-3\sqrt{-11})(8+3\sqrt{-11})$	$\mathbb{\mathbb{Z}}[\sqrt{11}]$	Prime
$\mathbb{\mathbb{Z}}[\sqrt{-13}]$	Irreducible	${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{13})}$
$\mathbb{\mathbb{Z}}[\sqrt{-14}]$		$\mathbb{\mathbb{Z}}[\sqrt{14}]$	$(87-23\sqrt{14})(87+23\sqrt{14})$
${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{-15})}$		$\mathbb{\mathbb{Z}}[\sqrt{15}]$	Irreducible
$\mathbb{\mathbb{Z}}[\sqrt{-17}]$		${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{17})}$	Prime
${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{-19})}$	$(12-\sqrt{-19})(12+\sqrt{-19})$	$\mathbb{\mathbb{Z}}[\sqrt{19}]$

Representation of 163 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	10100011	20001	2203	1123	431	322	243	201	163	139	117	C7	B9	AD	1A	9A	91	8B	83

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