A308675 a(n) = Sum_{d|n} d^(d^2 * n).

1, 257, 7625597484988, 340282366920938463463374607431768276993, 2350988701644575015937473074444491355637331113544175043017503412556834518909454345703126

Offset

1,2

Comments

The next term has 169 digits. - Harvey P. Dale, Feb 29 2020

Links

Table of n, a(n) for n=1..5.

Formula

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

Mathematica

Table[Total[#^(#^2 n)&/@Divisors[n]], {n, 5}] (* Harvey P. Dale, Feb 29 2020 *)
a[n_] := DivisorSum[n, #^(n * #^2) &]; Array[a, 5] (* Amiram Eldar, May 11 2021 *)

Prog

(PARI) {a(n) = sumdiv(n, d, d^(d^2*n))}
(PARI) N=10; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k^k^2*x)^k)^(1/k)))))

Crossrefs

Column k=3 of A308676.

Cf. A023887, A055225, A308670.

Sequence in context: A194155 A238614 A308672 * A121237 A161683 A250741

Adjacent sequences: A308672 A308673 A308674 * A308676 A308677 A308678

Keyword

nonn

Author

Seiichi Manyama, Jun 16 2019

Status

approved