A069914 a(n) = Sum_{d|n} (d-1)*sigma(n/d).

0, 1, 2, 6, 4, 15, 6, 23, 16, 27, 10, 64, 12, 39, 42, 72, 16, 98, 18, 110, 60, 63, 22, 213, 48, 75, 84, 156, 28, 245, 30, 201, 96, 99, 102, 380, 36, 111, 114, 357, 40, 345, 42, 248, 248, 135, 46, 618, 96, 278, 150, 294, 52, 478, 162, 501, 168, 171, 58, 924, 60, 183

Offset: 1

Author

Vladeta Jovovic, May 04 2002

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A006579, A007429, A060640.

Programs

Mathematica

Table[Plus @@ (DivisorSigma[1, ds = Divisors[n]]*(n/ds - 1)), {n, 62}] (* Ivan Neretin, May 17 2015 *)

PARI

a(n) = sumdiv(n, d, (d-1)*sigma(n/d)) \\ Michel Marcus, Jun 17 2013

Formula

a(n) = A060640(n) - A007429(n).

G.f.: Sum_{k>=1} sigma(k) * x^(2*k) / (1 - x^k)^2. - Ilya Gutkovskiy, Aug 19 2021