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# 110

Please do not rely on any information it contains.

110 is an integer.

## Membership in core sequences

 Even numbers ..., 104, 106, 108, 110, 112, 114, 116, ... A005843 Composite numbers ..., 105, 106, 108, 110, 111, 112, 114, ... A002808 Oblong numbers ..., 56, 72, 90, 110, 132, 156, 182, ... A002378 Quarter-squares ..., 81, 90, 100, 110, 121, 132, 144, ... A002620 Squarefree numbers ..., 106, 107, 109, 110, 111, 113, 114, ... A005117

## Sequences pertaining to 110

 Multiples of 110 0, 110, 220, 330, 440, 550, 660, 770, 880, ... Divisors of 110 1, 2, 5, 10, 11, 22, 55, 110 A018288 $3x+1$ sequence starting at 97 97, 292, 146, 73, 220, 110, 55, 166, 83, 250, ... A008873

## Partitions of 110

There are 607163746 partitions of 110.

The Goldbach representations of 110 are: 3 + 107 = 7 + 103 = 13 + 97 = 31 + 79 = 37 + 73 = 43 + 67.

## Values for number theoretic functions with 110 as an argument

 $\mu (110)$ −1 $M(110)$ −5 $\pi (110)$ 29 $\sigma _{1}(110)$ 216 $\sigma _{0}(110)$ 8 $\phi (110)$ 40 $\Omega (110)$ 3 $\omega (110)$ 3 $\lambda (110)$ This is the Carmichael lambda function. $\lambda (110)$ This is the Liouville lambda function.

PLACEHOLDER

## Factorization of 110 in some quadratic integer rings

As was mentioned above, 110 is the product of three distinct primes in $\mathbb {Z}$ . But in some quadratic integer rings, some of these primes are further reducible.

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## Representation of 110 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 1101110 11002 1232 420 302 215 156 132 110 A0 92 86 7C 75 6E 68 62 5F 5A

Notice that in base 10, we have 110 = 11 × 10. No smaller number has this property in decimal.

 $-1$ 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