A308672 a(n) = Sum_{d|n} d^(d^3).

1, 257, 7625597484988, 340282366920938463463374607431768211713, 2350988701644575015937473074444491355637331113544175043017503412556834518909454345703126

Offset: 1

Author

Seiichi Manyama, Jun 16 2019

Keywords

• nonn

Comments

The next term (a(6)) has 169 digits. - Harvey P. Dale, Sep 08 2020

Crossrefs

Column k=3 of A308674.

Cf. A000005, A062796, A308671.

Programs

Mathematica

Table[Total[Divisors[n]^Divisors[n]^3],{n,5}] (* Harvey P. Dale, Sep 08 2020 *)
a[n_] := DivisorSum[n, #^(#^3) &]; Array[a, 5] (* Amiram Eldar, May 11 2021 *)

PARI

{a(n) = sumdiv(n, d, d^d^3)}

PARI

N=10; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^(k^(k^3-1))))))

Formula

L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(k^3-1))) = Sum_{k>=1} a(k)*x^k/k.