This site is supported by donations to The OEIS Foundation.
170
170 is an integer.
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 170
- 3 Partitions of 170
- 4 Values for number theoretic functions with 170 as an argument
- 5 Factorization of some small integers in a quadratic integer ring adjoining the square root of −170 or 170
- 6 Factorization of 170 in some quadratic integer rings
- 7 Representation of 170 in various bases
- 8 See also
Membership in core sequences
Even numbers | ..., 164, 166, 168, 170, 172, 174, 176, ... | A005843 |
Composite numbers | ..., 166, 168, 169, 170, 171, 172, 174, ... | A002808 |
Squarefree numbers | ..., 165, 166, 167, 170, 173, 174, 177, ... | A005117 |
Sequences pertaining to 170
Multiples of 170 | 0, 170, 340, 510, 680, 850, 1020, 1190, 1360, 1530, 1700, 1870, 2040, ... | |
Divisors of 170 | 1, 2, 5, 10, 17, 34, 85, 170 | A018315 |
sequence starting at 75 | 75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1, 4, 2, 1, ... | A258056 |
Partitions of 170
There are 274768617130 partitions of 170.
The Goldbach representations of 170 are: 167 + 3 = 163 + 7 = 157 + 13 = 151 + 19 = 139 + 31 = 127 + 43 = 109 + 61 = 103 + 67 = 97 + 73.
Values for number theoretic functions with 170 as an argument
−1 | ||
−2 | ||
39 | ||
324 | ||
8 | ||
64 | ||
3 | ||
3 | ||
This is the Carmichael lambda function. | ||
This is the Liouville lambda function. |
Note that both and are square. This is not true for any smaller integer.
Factorization of some small integers in a quadratic integer ring adjoining the square root of −170 or 170
Neither nor are unique factorization domains; the former has class number 12 and the latter class number 4. The former has only −1 and 1 for units, the latter has infinitely many units, with as the fundamental unit, which has a norm of −1.
PLACEHOLDER FOR TABLE
Ideals really help us make sense of multiple distinct factorizations in these domains.
Factorization of | ||
In | In | |
2 | ||
3 | Prime | |
5 | ||
7 | Prime | |
11 | ||
13 | ||
17 | ||
19 | Prime | |
23 | ||
29 | ||
31 | ||
37 | ||
41 | ||
43 | ||
47 |
Factorization of 170 in some quadratic integer rings
As was mentioned above, 170 is the product of three distinct primes in . But in some quadratic integer rings, some of these primes are further reducible.
TABLE GOES HERE
Representation of 170 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 10101010 | 20022 | 2222 | 1140 | 442 | 332 | 252 | 208 | 170 | 145 | 122 | 101 | C2 | B5 | AA | A0 | 98 | 8I | 8A |
As you can see, this number is a repdigit in quartal and hexadecimal, as well as in base 33 (as 55). It is of course a repunit in base 169.
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 |