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%I #17 Nov 20 2022 01:55:27
%S 1,29,67,401,221,1943,519,4177,2398,6409,1739,26867,2757,15051,14807,
%T 38145,5849,69542,8019,88621,34773,50431,13847,279859,30896,79953,
%U 71194,208119,27029,429403,32799,326337,116513,169621,114699,961598,54909,232551,184719,923117,74129,1008417,85227,697339
%N a(n) = n * Sum_{d|n} sigma(d)^3 / d.
%H Amiram Eldar, <a href="/A344043/b344043.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k >= 1} sigma(k)^3 * x^k/(1 - x^k)^2.
%F Sum_{k=1..n} a(k) ~ c * n^4, where c = (Pi^6*zeta(3)^2/2160) * Product_{p prime} (1 + 2/p^2 + 2/p^3 + 1/p^5) = 1.8238925519... . - _Amiram Eldar_, Nov 20 2022
%t a[n_] := n * DivisorSum[n, DivisorSigma[1, #]^3/# &]; Array[a, 44] (* _Amiram Eldar_, May 08 2021 *)
%o (PARI) a(n) = n*sumdiv(n, d, sigma(d)^3/d);
%o (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k)^3*x^k/(1-x^k)^2))
%Y Cf. A002117, A060640, A226565, A226566, A344044.
%K nonn,mult
%O 1,2
%A _Seiichi Manyama_, May 08 2021
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