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a(n) = Sum_{d|n} d^(3*d).
4

%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