A078308 a(n) = Sum_{d divides n} d^(n/d + 1).

1, 5, 10, 25, 26, 80, 50, 161, 163, 290, 122, 988, 170, 796, 1580, 2305, 290, 5561, 362, 10670, 9404, 5912, 530, 58436, 16251, 19258, 66340, 118640, 842, 381740, 962, 431105, 547172, 268214, 509500, 3534037, 1370, 1056880, 4813052, 8616326, 1682

Offset: 1

Author

Vladeta Jovovic, Nov 22 2002

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..6284

Crossrefs

Cf. A055225, A006906, A022661.

Programs

Maple

A078308 := proc(n)
        add( d^(n/d+1),d=numtheory[divisors](n)) ;
end proc:
seq(A078308(n),n=1..10) ; # R. J. Mathar, Dec 14 2011

Mathematica

Table[CoefficientList[Series[-Log[Product[(1 - k x^k), {k, 1, 60}]], {x, 0, 60}],x][[n + 1]] (n), {n, 1, 60}] (* Benedict W. J. Irwin, Jul 04 2016 *)
Table[Total[#^(n/#+1)&/@Divisors[n]],{n,50}] (* Harvey P. Dale, Aug 02 2025 *)

PARI

a(n) = sumdiv(n, d, d^(n/d+1)); \\ Michel Marcus, Jul 04 2016

PARI

N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, 1-k*x^k)))) \\ Seiichi Manyama, Jun 02 2019

Formula

G.f.: Sum_{n>0} n^2*x^n/(1-n*x^n).

L.g.f.: -log(Product_{ k>0 } (1-k*x^k)) = Sum_{ n>=0 } (a(n)/n)*x^n. - Benedict W. J. Irwin, Jul 04 2016