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%I #20 May 09 2021 02:50:44
%S 1,65,19684,16777281,30517578126,101559956688164,558545864083284008,
%T 4722366482869661990977,58149737003040059690409853,
%U 1000000000000000000030517578190,23225154419887808141001767796309132,708801874985091845381344408569542626596
%N a(n) = Sum_{d|n} d^(3*d).
%H Seiichi Manyama, <a href="/A308697/b308697.txt">Table of n, a(n) for n = 1..152</a>
%F L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(3*k-1))) = Sum_{k>=1} a(k)*x^k/k.
%F G.f.: Sum_{k>=1} k^(3*k) * x^k/(1 - x^k).
%t a[n_] := DivisorSum[n, #^(3*#) &]; Array[a, 12] (* _Amiram Eldar_, May 09 2021 *)
%o (PARI) {a(n) = sumdiv(n, d, d^(3*d))}
%o (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(3*k-1)))))
%o (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(3*k)*x^k/(1-x^k)))
%Y Column k=3 of A308698.
%Y Cf. A073706, A308757.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jun 17 2019
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