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.
%I A308689 #22 May 09 2021 02:51:08
%S A308689 1,3,4,21,6,216,8,1289,2197,8828,12,142278,14,526704,1672464,5246993,
%T A308689 18,76887669,20,345319966,1163085032,2147498312,24,52918480178,
%U A308689 1220703151,137438982060,847293392440,1374672048414,30,31838544112466,32,87962004029473
%N A308689 a(n) = Sum_{d|n} d^(3*n/d - 2).
%H A308689 Seiichi Manyama, <a href="/A308689/b308689.txt">Table of n, a(n) for n = 1..1000</a>
%F A308689 L.g.f.: -log(Product_{k>=1} (1 - k^3*x^k)^(1/k^3)) = Sum_{k>=1} a(k)*x^k/k.
%F A308689 a(p) = p+1 for prime p.
%F A308689 G.f.: Sum_{k>=1} k*x^k/(1 - k^3*x^k). - _Ilya Gutkovskiy_, Jul 25 2019
%t A308689 a[n_] := DivisorSum[n, #^(3*n/# - 2) &]; Array[a, 32] (* _Amiram Eldar_, May 09 2021 *)
%o A308689 (PARI) {a(n) = sumdiv(n, d, d^(3*n/d-2))}
%o A308689 (PARI) N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k^3*x^k)^(1/k^3)))))
%Y A308689 Column k=3 of A308690.
%Y A308689 Cf. A308692, A308693.
%K A308689 nonn
%O A308689 1,2
%A A308689 _Seiichi Manyama_, Jun 17 2019