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170

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Please do not rely on any information it contains.            


170 is an integer.

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

Some integers
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