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A294645 a(n) = Sum_{d|n} d^(n+1).

%I A294645 #39 Feb 16 2025 08:33:51
%S A294645 1,9,82,1057,15626,282252,5764802,134480385,3486843451,100048830174,
%T A294645 3138428376722,107006334784468,3937376385699290,155572843119354936,
%U A294645 6568408508343827972,295150156996346511361,14063084452067724991010,708236696816416252145973
%N A294645 a(n) = Sum_{d|n} d^(n+1).
%H A294645 Seiichi Manyama, <a href="/A294645/b294645.txt">Table of n, a(n) for n = 1..385</a>
%H A294645 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>
%F A294645 G.f.: Sum_{k>0} k^(k+1)*x^k/(1-(k*x)^k).
%F A294645 L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)) = Sum_{k>=1} a(k)*x^k/k. - _Seiichi Manyama_, Jun 02 2019
%F A294645 a(n) ~ n^(n+1). - _Vaclav Kotesovec_, Oct 07 2020
%t A294645 Table[DivisorSigma[n + 1, n], {n, 1, 20}] (* _Vaclav Kotesovec_, Oct 07 2020 *)
%o A294645 (PARI) {a(n) = sigma(n, n+1)}
%o A294645 (PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, k^(k+1)*x^k/(1-(k*x)^k)))
%o A294645 (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, 1-(k*x)^k)))) \\ _Seiichi Manyama_, Jun 02 2019
%Y A294645 Column k=1 of A308504.
%Y A294645 Cf. A023882, A023887, A082245, A158095, A292312.
%K A294645 nonn
%O A294645 1,2
%A A294645 _Seiichi Manyama_, Nov 05 2017