161

This article is under construction.            

Please do not rely on any information it contains.            

161 is an integer. It is a Cullen number, corresponding to $n=5$.

Membership in core sequences

Odd numbers	..., 155, 157, 159, 161, 163, 165, 167, ...	A005408
Semiprimes	..., 155, 158, 159, 161, 166, 169, 177, ...	A001358
Composite numbers	..., 158, 159, 160, 161, 162, 164, 165, ...	A002808
Squarefree numbers	..., 157, 158, 159, 161 163, 165, 166, ...	A005117

Sequences pertaining to 161

Multiples of 161	0, 161, 322, 483, 644, 805, 966, 1127, 1288, 1449, 1610, 1771, 1932, ...
$3x+1$ sequence beginning at 27	..., 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, ...

Partitions of 161

There are 118159068427 partitions of 161.

Roots and powers of 161

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

TABLE GOES HERE

Values for number theoretic functions with 161 as an argument

$\mu (161)$	1
$M(161)$	1
$\pi (161)$	37
$\sigma _{1}(161)$	192
$\sigma _{0}(161)$	4
$\phi (161)$	132
$\Omega (161)$	2
$\omega (161)$	2
$\lambda (161)$		This is the Carmichael lambda function.
$\lambda (161)$	1	This is the Liouville lambda function.

Notice that $\phi (161)=132$, which is clearly not a divisor of 160. This means 161 is a composite Cullen number which does not have the Lehmer property.

Factorization of some small integers in a quadratic integer ring adjoining the square roots of −161, 161

REMARKS GO HERE. Fundamental unit $11775+928{\sqrt {161}}$.

$n$	$\mathbb {Z} [{\sqrt {-161}}]$	${\mathcal {O}}_{\mathbb {Q} ({\sqrt {161}})}$
2	Irreducible	$\left({\frac {13}{2}}-{\frac {\sqrt {161}}{2}}\right)\left({\frac {13}{2}}+{\frac {\sqrt {161}}{2}}\right)$
3		Prime
4	2 2	$\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)^{2}$
5	Irreducible	$(-1)(38-3{\sqrt {161}})(38+3{\sqrt {161}})$
6	2 × 3	$\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)3$
7	Irreducible	$(-1)(203-16{\sqrt {161}})(203+16{\sqrt {161}})$
8	2 3	$\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)^{3}$
9	3 2
10	2 × 5	$(-1)\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)(38\pm 3{\sqrt {161}})$
11	Irreducible	Prime
12	2 2 × 3	$\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)^{2}3$
13	Prime
14	2 × 7	$(-1)\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)(203\pm 16{\sqrt {161}})$
15	3 × 5	$(-1)3(38\pm 3{\sqrt {161}})$
16	2 4	$\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)^{4}$
17	Irreducible	$(-1)(12-{\sqrt {161}})(12+{\sqrt {161}})$
18	2 2 × 3 2	$\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)3^{2}$
19	Prime
20	2 2 × 5	$(-1)\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)^{2}(38\pm 3{\sqrt {161}})$
21	3 × 7	$(-1)3(203\pm 16{\sqrt {161}})$
22	2 × 11	$\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)11$
23	Irreducible	$(368-29{\sqrt {161}})(368+29{\sqrt {161}})$
24	2 3 × 3	$\left({\frac {13}{2}}\pm {\frac {\sqrt {161}}{2}}\right)^{3}3$
25	5 2	$(38\pm 3{\sqrt {161}})^{2}$

Factorization of 161 in some quadratic integer rings

As was mentioned above, 161 is a semiprime in $\mathbb {Z}$. But it has different factorizations in some quadratic integer rings.

TABLE GOES HERE

Representation of 161 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	10100001	12222	2201	1121	425	320	241	188	161	137	115	C5	B7	AB	A1	98	8H	89	81

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