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.

A308696 a(n) = Sum_{d|n} d^(2*d).

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%I A308696 #21 May 09 2021 02:50:50
%S A308696 1,17,730,65553,9765626,2176783082,678223072850,281474976776209,
%T A308696 150094635296999851,100000000000009765642,81402749386839761113322,
%U A308696 79496847203390846310290154,91733330193268616658399616010,123476695691247935826908004929122
%N A308696 a(n) = Sum_{d|n} d^(2*d).
%H A308696 Seiichi Manyama, <a href="/A308696/b308696.txt">Table of n, a(n) for n = 1..214</a>
%F A308696 L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(2*k-1))) = Sum_{k>=1} a(k)*x^k/k.
%F A308696 G.f.: Sum_{k>=1} k^(2*k) * x^k/(1 - x^k).
%t A308696 a[n_] := DivisorSum[n, #^(2*#) &]; Array[a, 14] (* _Amiram Eldar_, May 09 2021 *)
%o A308696 (PARI) {a(n) = sumdiv(n, d, d^(2*d))}
%o A308696 (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(2*k-1)))))
%o A308696 (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(2*k)*x^k/(1-x^k)))
%Y A308696 Column k=2 of A308698.
%Y A308696 Cf. A073705, A308753, A308756.
%K A308696 nonn
%O A308696 1,2
%A A308696 _Seiichi Manyama_, Jun 17 2019