login
A359103
a(n) = Sum_{d|n} d * (n/d)^d.
4
1, 4, 6, 16, 10, 54, 14, 112, 99, 230, 22, 996, 26, 1022, 1620, 3232, 34, 9828, 38, 18100, 16380, 22814, 46, 133272, 15675, 106886, 179388, 354116, 58, 1218150, 62, 1589824, 1952676, 2228870, 630980, 13767264, 74, 9962270, 20732868, 34787000, 82, 113676402, 86
OFFSET
1,2
LINKS
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