A069913 a(n) = Sum_{d|n} (d-1)*tau(n/d).

0, 1, 2, 5, 4, 11, 6, 16, 12, 19, 10, 37, 12, 27, 26, 42, 16, 54, 18, 59, 36, 43, 22, 100, 32, 51, 48, 81, 28, 113, 30, 99, 56, 67, 54, 162, 36, 75, 66, 152, 40, 153, 42, 125, 108, 91, 46, 240, 60, 134, 86, 147, 52, 202, 82, 204, 96, 115, 58, 331, 60, 123, 144, 219, 96

Offset: 1

Author

Vladeta Jovovic, May 04 2002

Keywords

• nonn

Crossrefs

Cf. A000005, A006579, A007425, A007429.

Programs

Mathematica

Table[DivisorSum[n,(#-1)DivisorSigma[0,n/#]&],{n,100}] (* Giorgos Kalogeropoulos, Aug 19 2021 *)

PARI

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

Formula

a(n) = A007429(n) - A007425(n).

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