login
a(n) = Sum_{d|n} sigma(d)^n.
3

%I #12 May 08 2021 23:06:55

%S 1,10,65,2483,7777,2990810,2097153,2568661988,10604761518,

%T 3570527751850,743008370689,232227195048256531,793714773254145,

%U 21035724521219881850,504857283427304833025,727429690188773950335429,2185911559738696531969,43567528891100073055151954340,5242880000000000000000001

%N a(n) = Sum_{d|n} sigma(d)^n.

%F G.f.: Sum_{k >= 1} (sigma(k) * x)^k/(1 - (sigma(k) * x)^k).

%F If p is prime, a(p) = 1 + (p+1)^p.

%t a[n_] := DivisorSum[n, DivisorSigma[1 , #]^n &]; Array[a, 19] (* _Amiram Eldar_, May 08 2021 *)

%o (PARI) a(n) = sumdiv(n, d, sigma(d)^n);

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (sigma(k)*x)^k/(1-(sigma(k)*x)^k)))

%Y Cf. A007429, A023887, A065018, A342471, A344044, A344047, A344061.

%K nonn

%O 1,2

%A _Seiichi Manyama_, May 08 2021