A344060 a(n) = Sum_{d|n} sigma(d)^n.
1, 10, 65, 2483, 7777, 2990810, 2097153, 2568661988, 10604761518, 3570527751850, 743008370689, 232227195048256531, 793714773254145, 21035724521219881850, 504857283427304833025, 727429690188773950335429, 2185911559738696531969, 43567528891100073055151954340, 5242880000000000000000001
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, DivisorSigma[1 , #]^n &]; Array[a, 19] (* Amiram Eldar, May 08 2021 *)
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PARI
a(n) = sumdiv(n, d, sigma(d)^n);
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (sigma(k)*x)^k/(1-(sigma(k)*x)^k)))
Formula
G.f.: Sum_{k >= 1} (sigma(k) * x)^k/(1 - (sigma(k) * x)^k).
If p is prime, a(p) = 1 + (p+1)^p.