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A174472 a(n) = Sum_{d|n} d^sigma(d). 5
1, 9, 82, 16393, 15626, 2176782426, 5764802, 35184372105225, 2541865828411, 1000000000000015634, 3138428376722, 1648446623609512543953220489306, 3937376385699290, 3214199700417740936756852426, 16834112196028232574462906332, 21267647932558653966460948148857618441 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

Logarithmic derivative of A174471.

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

MATHEMATICA

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

PROG

(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

CROSSREFS

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

Sequence in context: A041146 A320991 A015497 * A039357 A048353 A037502

Adjacent sequences:  A174469 A174470 A174471 * A174473 A174474 A174475

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 04 2010

STATUS

approved

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Last modified August 19 18:30 EDT 2022. Contains 356229 sequences. (Running on oeis4.)