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161
From OeisWiki
161 is an integer. It is a Cullen number, corresponding to .
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 161
- 3 Partitions of 161
- 4 Roots and powers of 161
- 5 Values for number theoretic functions with 161 as an argument
- 6 Factorization of some small integers in a quadratic integer ring adjoining the square roots of −161, 161
- 7 Factorization of 161 in some quadratic integer rings
- 8 Representation of 161 in various bases
- 9 See also
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, ... | |
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
1 | ||
1 | ||
37 | ||
192 | ||
4 | ||
132 | ||
2 | ||
2 | ||
This is the Carmichael lambda function. | ||
1 | This is the Liouville lambda function. |
Notice that , 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 .
2 | Irreducible | |
3 | Prime | |
4 | 2 2 | |
5 | Irreducible | |
6 | 2 × 3 | |
7 | Irreducible | |
8 | 2 3 | |
9 | 3 2 | |
10 | 2 × 5 | |
11 | Irreducible | Prime |
12 | 2 2 × 3 | |
13 | Prime | |
14 | 2 × 7 | |
15 | 3 × 5 | |
16 | 2 4 | |
17 | Irreducible | |
18 | 2 2 × 3 2 | |
19 | Prime | |
20 | 2 2 × 5 | |
21 | 3 × 7 | |
22 | 2 × 11 | |
23 | Irreducible | |
24 | 2 3 × 3 | |
25 | 5 2 |
Factorization of 161 in some quadratic integer rings
As was mentioned above, 161 is a semiprime in . 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
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 |