A174472 a(n) = Sum_{d|n} d^sigma(d).

1, 9, 82, 16393, 15626, 2176782426, 5764802, 35184372105225, 2541865828411, 1000000000000015634, 3138428376722, 1648446623609512543953220489306, 3937376385699290, 3214199700417740936756852426, 16834112196028232574462906332, 21267647932558653966460948148857618441

Offset: 1

Author

Paul D. Hanna, Apr 04 2010

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..167

Crossrefs

Cf. A000203 (sigma), A062796, A174471, A174937, A345895.

Programs

Mathematica

a[n_] := DivisorSum[n, #^DivisorSigma[1, #] &]; Array[a, 16] (* Amiram Eldar, Oct 08 2021 *)

PARI

{a(n)=sumdiv(n,d,d^sigma(d))}

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^sigma(k)*x^k/(1-x^k))) \\ Seiichi Manyama, Oct 14 2021

Formula

Logarithmic derivative of A174471.

G.f.: Sum_{k>=1} k^sigma(k) * x^k/(1 - x^k). - Seiichi Manyama, Oct 14 2021