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
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..386
Programs
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PARI
a(n) = sum(k=1, n, sigma(k, n)*(n\k));
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PARI
a(n) = sum(k=1, n, sumdiv(k, d, d^n*numdiv(k/d)));
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PARI
a(n) = sum(k=1, n, sumdiv(k, d, sigma(d, n)));
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