OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..5000
FORMULA
a(n) = n * A087909(n).
G.f.: Sum_{k>=1} k * x^k/(1 - k * x^k)^2.
If p is prime, a(p) = 2 * p.
a(n) = [x^n] Sum_{k>0} k * (n * x / k)^k / (1 - x^k). - Seiichi Manyama, Jan 16 2023
MATHEMATICA
a[n_] := DivisorSum[n, (n/#)^#*# &]; Array[a, 43] (* Amiram Eldar, Aug 27 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, d*(n/d)^d);
(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-k*x^k)^2))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 17 2022
STATUS
approved