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

Author

Jaroslav Krizek, Sep 16 2018

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A000040, A000203, A007429, A221219.

Programs

Magma

[&+[SumOfDivisors(d): d in Divisors(n)] mod  SumOfDivisors(n): n in [1..1000]];

Mathematica

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

PARI

A319296(n) = (sumdiv(n,d,sigma(d))%sigma(n)); \\ Antti Karttunen, Sep 16 2018

Formula

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

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.