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%I #17 Aug 27 2023 17:02:28
%S 1,6,29,299,3127,48360,823545,16918164,387462126,10019541652,
%T 285311670613,8920567022545,302875106592255,11113363273445312,
%U 437893951476881153,18447309245488431653,827240261886336764179,39346708488214110663954,1978419655660313589123981
%N a(n) = Sum_{d|n} sigma_d(d)^(n/d).
%H Seiichi Manyama, <a href="/A359053/b359053.txt">Table of n, a(n) for n = 1..386</a>
%F G.f.: Sum_{k >= 1} sigma_k(k) * x^k/(1 - sigma_k(k) * x^k).
%F If p is prime, a(p) = 2 + p^p.
%t a[n_] := DivisorSum[n, DivisorSigma[#, #]^(n/#) &]; Array[a, 19] (* _Amiram Eldar_, Aug 27 2023 *)
%o (PARI) a(n) = sumdiv(n, d, sigma(d, d)^(n/d));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k, k)*x^k/(1-sigma(k, k)*x^k)))
%Y Cf. A344061, A359052, A359054.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Dec 14 2022
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