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# 35

Please do not rely on any information it contains.

35 is an integer.

## Membership in core sequences

 Odd numbers ..., 29, 31, 33, 35, 37, 39, 41, ... A005843 Semiprimes ..., 26, 33, 34, 35, 38, 39, 46, ... A001358 Squarefree numbers ..., 31, 33, 34, 35, 37, 38, 39, ... A005117 Composite numbers ..., 32, 33, 34, 35, 36, 38, 39, ... A002808 Tetrahedral numbers ..., 4, 10, 20, 35, 56, 84, 120, ... A000292 Pentagonal numbers ..., 5, 12, 22, 35, 51, 70, 92, ... A000326

In Pascal's triangle, 35 occurs four times, the first two times on the seventh row as the sum of 15 and 20 on the sixth row.

## Sequences pertaining to 35

 Multiples of 35 0, 35, 70, 105, 140, 175, 210, 245, 280, 315, ... 35-gonal numbers 1, 35, 102, 202, 335, 501, 700, 932, 1197, 1495, ... $3x+1$ sequence starting at 15 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, ... A033480 $3x-1$ sequence starting at 63 63, 188, 94, 47, 140, 70, 35, 104, 52, 26, 13, ... A008895

## Partitions of 35

There are 14883 partitions of 35. Of these, [FINISH WRITING]

## Roots and powers of 35

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

 ${\sqrt {35}}$ 5.91607978 A010490 35 2 1225 ${\sqrt[{3}]{35}}$ 3.27106631 A010606 35 3 42875 ${\sqrt[{4}]{35}}$ 2.43229927 A011030 35 4 1500625 ${\sqrt[{5}]{35}}$ 2.03616800 A011120 35 5 52521875 ${\sqrt[{6}]{35}}$ 1.80860894 35 6 1838265625 ${\sqrt[{7}]{35}}$ 1.66180916 35 7 64339296875 ${\sqrt[{8}]{35}}$ 1.55958304 35 8 2251875390625 ${\sqrt[{9}]{35}}$ 1.48444159 35 9 78815638671875 ${\sqrt[{10}]{35}}$ 1.42694358 35 10 2758547353515625 A009979

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## Values for number theoretic functions with 35 as an argument

 $\mu (35)$ 1 $M(35)$ −1 $\pi (35)$ 11 $\sigma _{1}(35)$ 48 $\sigma _{0}(35)$ 4 $\phi (35)$ 24 $\Omega (35)$ 2 $\omega (35)$ 2 $\lambda (35)$ This is the Carmichael lambda function. $\lambda (35)$ This is the Liouville lambda function. $\zeta (35)$ 1.00000000002910385044497099686929425227884... 35! 10333147966386144929666651337523200000000 $\Gamma (35)$ 295232799039604140847618609643520000000

## Factorization of some small integers in a quadratic integer ring adjoining −35, 35

Neither ${\mathcal {O}}_{\mathbb {Q} ({\sqrt {-35}})}$ nor $\mathbb {Z} [{\sqrt {35}}]$ are unique factorization domains, they both have class number 2. $\mathbb {Z} [{\sqrt {35}}]$ has units of the form $\pm (6+{\sqrt {35}})^{n}\,$ ($n\in \mathbb {Z}$ ).

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PLACEHOLDER

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## Representation of 35 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 100011 1022 203 120 55 50 43 38 35 2D 32 29 27 25 23 21 1H 1G 1F

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 $-1$ 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