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A356046 a(n) = Sum_{k=1..n} sigma_n(k) * floor(n/k).

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%I A356046 #17 Aug 07 2022 03:54:38
%S A356046 1,7,40,393,4498,68898,1205205,24830617,574911611,14936215765,
%T A356046 427782762142,13426870089265,457622727372932,16842615801316402,
%U A356046 665489035541044561,28102162770144986248,1262904298391426474369,60182778141796948356895
%N A356046 a(n) = Sum_{k=1..n} sigma_n(k) * floor(n/k).
%H A356046 Seiichi Manyama, <a href="/A356046/b356046.txt">Table of n, a(n) for n = 1..386</a>
%F A356046 a(n) = [x^n] (1/(1-x)) * Sum_{k>=1} sigma_n(k) * x^k/(1 - x^k).
%F A356046 a(n) = Sum_{k=1..n} Sum_{d|k} d^n * tau(k/d).
%F A356046 a(n) = Sum_{k=1..n} Sum_{d|k} sigma_n(d).
%F A356046 a(n) ~ c * n^n, where c = 1/(1 - 1/exp(1)) = A185393. - _Vaclav Kotesovec_, Aug 07 2022
%o A356046 (PARI) a(n) = sum(k=1, n, sigma(k, n)*(n\k));
%o A356046 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, d^n*numdiv(k/d)));
%o A356046 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, sigma(d, n)));
%Y A356046 Cf. A321141, A356045.
%K A356046 nonn
%O A356046 1,2
%A A356046 _Seiichi Manyama_, Jul 24 2022