cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A308697 a(n) = Sum_{d|n} d^(3*d).

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