A087909 a(n) = Sum_{d|n} (n/d)^(d-1).

1, 2, 2, 4, 2, 9, 2, 14, 11, 23, 2, 83, 2, 73, 108, 202, 2, 546, 2, 905, 780, 1037, 2, 5553, 627, 4111, 6644, 12647, 2, 40605, 2, 49682, 59172, 65555, 18028, 382424, 2, 262165, 531612, 869675, 2, 2706581, 2, 3147083, 5180382, 4194329, 2, 27246533, 117651

Offset: 1

Author

Vladeta Jovovic, Oct 15 2003

Keywords

• nonn
• look

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..6290

Crossrefs

Cf. A055225, A078308.

Programs

Mathematica

a[n_]:= DivisorSum[n, (n/#)^(#-1) &]; Array[a, 30] (* G. C. Greubel, May 16 2018 *)

PARI

a(n)=sumdiv(n, d, d^(n/d-1) );  /* Joerg Arndt, Oct 07 2012 */

PARI

N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k*x^k)^(1/k^2))))) \\ Seiichi Manyama, Jun 17 2019

Formula

G.f.: Sum_{k>0} x^k/(1-k*x^k).

From Seiichi Manyama, Jun 17 2019: (Start)

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

a(p) = 2 for prime p. (End)