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A356046

a(n) = Sum_{k=1..n} sigma_n(k) * floor(n/k).

1, 7, 40, 393, 4498, 68898, 1205205, 24830617, 574911611, 14936215765, 427782762142, 13426870089265, 457622727372932, 16842615801316402, 665489035541044561, 28102162770144986248, 1262904298391426474369, 60182778141796948356895

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OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..386

FORMULA

a(n) = [x^n] (1/(1-x)) * Sum_{k>=1} sigma_n(k) * x^k/(1 - x^k).

a(n) = Sum_{k=1..n} Sum_{d|k} d^n * tau(k/d).

a(n) = Sum_{k=1..n} Sum_{d|k} sigma_n(d).

a(n) ~ c * n^n, where c = 1/(1 - 1/exp(1)) = A185393. - Vaclav Kotesovec, Aug 07 2022

PROG

(PARI) a(n) = sum(k=1, n, sigma(k, n)*(n\k));

(PARI) a(n) = sum(k=1, n, sumdiv(k, d, d^n*numdiv(k/d)));

(PARI) a(n) = sum(k=1, n, sumdiv(k, d, sigma(d, n)));

CROSSREFS

Cf. A321141, A356045.

Sequence in context: A391378 A356459 A226223 * A385059 A062727 A223416

Adjacent sequences: A356043 A356044 A356045 * A356047 A356048 A356049

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jul 24 2022

STATUS

approved

URL: https://oeis.org/A356046

⇱ A356046 - OEIS