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A294956 a(n) = Sum_{d|n} d^(d + n/d).

%I A294956 #29 Jan 11 2023 06:46:35
%S A294956 1,9,82,1041,15626,280212,5764802,134221889,3486785131,100000078254,
%T A294956 3138428376722,106993207077516,3937376385699290,155568095598166344,
%U A294956 6568408355713287812,295147905180426634241,14063084452067724991010
%N A294956 a(n) = Sum_{d|n} d^(d + n/d).
%H A294956 Seiichi Manyama, <a href="/A294956/b294956.txt">Table of n, a(n) for n = 1..385</a>
%F A294956 L.g.f.: -log(Product_{k>=1} (1 - k*x^k)^(k^(k-1))) = Sum_{k>=1} a(k)*x^k/k. - _Seiichi Manyama_, Jun 09 2019
%F A294956 G.f.: Sum_{k>0} k^(k+1) * x^k / (1 - k * x^k). - _Seiichi Manyama_, Jan 11 2023
%t A294956 sd[n_]:=Total[#^(#+n/#)&/@Divisors[n]]; Array[sd,20] (* _Harvey P. Dale_, Mar 28 2021 *)
%o A294956 (PARI) a(n) = sumdiv(n, d, d^(d+n/d));
%o A294956 (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k*x^k)^(k^(k-1)))))) \\ _Seiichi Manyama_, Jun 09 2019
%o A294956 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k+1)*x^k/(1-k*x^k))) \\ _Seiichi Manyama_, Jan 11 2023
%Y A294956 Cf. A055225, A062796, A294957.
%K A294956 nonn
%O A294956 1,2
%A A294956 _Seiichi Manyama_, Nov 12 2017