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%I #33 Jun 19 2022 15:22:55
%S 1,17,730,65601,9765626,2176802276,678223072850,281474993488897,
%T 150094635297530563,100000000030517582222,81402749386839761113322,
%U 79496847203492408399442540,91733330193268616658399616010,123476695691248494372093865205800
%N a(n) = Sum_{d|n} d^(d+n).
%H Seiichi Manyama, <a href="/A308594/b308594.txt">Table of n, a(n) for n = 1..214</a>
%F L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)^(k^(k-1))) = Sum_{k>=1} a(k)*x^k/k.
%F G.f.: Sum_{k>=1} (k^2 * x)^k/(1 - (k * x)^k). - _Seiichi Manyama_, Mar 16 2021
%t sp[n_]:=Module[{d=Divisors[n]},Table[d[[k]]^(d[[k]]+n),{k,Length[ d]}]] // Total; Array[sp,15] (* _Harvey P. Dale_, Jan 02 2020 *)
%t a[n_] := DivisorSum[n, #^(# + n) &]; Array[a, 14] (* _Amiram Eldar_, May 11 2021 *)
%o (PARI) a(n) = sumdiv(n, d, d^(d+n));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(x*deriv(-log(prod(k=1, N, (1-(k*x)^k)^(k^(k-1))))))
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k^2*x)^k/(1-(k*x)^k))) \\ _Seiichi Manyama_, Mar 16 2021
%o (Python)
%o from sympy import divisors
%o def A308594(n): return sum(d**(d+n) for d in divisors(n,generator=True)) # _Chai Wah Wu_, Jun 19 2022
%Y Cf. A062796, A294956, A308668.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jun 09 2019
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