A319296 a(n) = (Sum_{d|n} (sigma(d))) mod sigma(n).

0, 1, 1, 4, 1, 8, 1, 11, 5, 10, 1, 27, 1, 12, 11, 26, 1, 33, 1, 35, 13, 16, 1, 10, 7, 18, 18, 43, 1, 68, 1, 57, 17, 22, 15, 16, 1, 24, 19, 2, 1, 84, 1, 59, 48, 28, 1, 37, 9, 59, 23, 67, 1, 112, 19, 114, 25, 34, 1, 49, 1, 36, 58, 120, 21, 116, 1, 83, 29, 108

Offset

1,4

Comments

a(n) = A007429(n) mod A000203(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(A221219(n)) = 0.

a(A000040(n)) = 1; the only composite number < 2*10^6 with a(n) = 1 is 636.

a(n) = n only for numbers 4, 10 and 96 < 3000000.

Example

For n = 4; a(4) = ((sigma(1) + sigma(2) + sigma(4)) mod sigma(4) = (1+3+7) mod 7 = 11 mod 7 = 4.

Mathematica

Table[Mod[Sum[DivisorSigma[1, d], {d, Divisors[n]}], DivisorSigma[1, n]], {n, 1, 100}] (* Vaclav Kotesovec, Sep 26 2018 *)

Prog

(Magma) [&+[SumOfDivisors(d): d in Divisors(n)] mod  SumOfDivisors(n): n in [1..1000]]
(PARI) A319296(n) = (sumdiv(n, d, sigma(d))%sigma(n)); \\ Antti Karttunen, Sep 16 2018

Crossrefs

Cf. A000203, A007429, A221219.

Sequence in context: A040019 A240776 A019768 * A211779 A318445 A158496

Adjacent sequences: A319293 A319294 A319295 * A319297 A319298 A319299

Keyword

nonn

Author

Jaroslav Krizek, Sep 16 2018

Status

approved