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%I #25 May 08 2021 06:26:17
%S 1,5,82,4101,390626,60466262,13841287202,4398046515205,
%T 1853020188851923,1000000000000390630,672749994932560009202,
%U 552061438912436478063702,542800770374370512771595362,629983141281877223617054459942
%N a(n) = Sum_{d|n} d^(2*(d-1)).
%H Seiichi Manyama, <a href="/A308753/b308753.txt">Table of n, a(n) for n = 1..215</a>
%F L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(2*k-3))) = Sum_{k>=1} a(k)*x^k/k.
%F G.f.: Sum_{k>=1} k^(2*(k-1)) * x^k/(1 - x^k).
%t a[n_] := DivisorSum[n, #^(2*(# - 1)) &]; Array[a, 14] (* _Amiram Eldar_, May 08 2021 *)
%o (PARI) {a(n) = sumdiv(n, d, d^(2*(d-1)))}
%o (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(2*k-3)))))
%o (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(2*(k-1))*x^k/(1-x^k)))
%Y Column k=2 of A308701.
%Y Cf. A283533, A308692, A308696, A308755, A308756.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jun 22 2019
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