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 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