A308671 - OEIS

%I #16 May 11 2021 01:54:27

%S 1,17,19684,4294967313,298023223876953126,

%T 10314424798490535546171968756,

%U 256923577521058878088611477224235621321608,6277101735386680763835789423207666416102355444468329480209

%N a(n) = Sum_{d|n} d^(d^2).

%F L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(k^2-1))) = Sum_{k>=1} a(k)*x^k/k.

%t a[n_] := DivisorSum[n, #^(#^2) &]; Array[a, 8] (* _Amiram Eldar_, May 11 2021 *)

%o (PARI) {a(n) = sumdiv(n, d, d^d^2)}

%o (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^(k^(k^2-1))))))

%Y Column k=2 of A308674.

%Y Cf. A000005, A062796, A308670.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 16 2019