A338662 a(n) = Sum_{d|n} (n/d)^d * binomial(d+n/d-1, d).

1, 5, 10, 29, 26, 123, 50, 305, 352, 668, 122, 3844, 170, 2593, 9704, 13825, 290, 41598, 362, 118259, 107986, 33047, 530, 929102, 394376, 130744, 1203580, 2737415, 842, 9910225, 962, 13315073, 14199222, 2404670, 33547310, 136502007, 1370, 10555795, 168405072, 548460064, 1682

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Formula

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

If p is prime, a(p) = 1 + p^2.

Mathematica

a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* Amiram Eldar, Apr 22 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^d*binomial(d+n/d-1, d));
(PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, 1/(1-k*x^k)^k-1))

Crossrefs

Cf. A081543, A338663, A343574.

Sequence in context: A134129 A240515 A105862 * A093029 A105505 A005514

Adjacent sequences: A338659 A338660 A338661 * A338663 A338664 A338665

Keyword

nonn

Author

Seiichi Manyama, Apr 22 2021

Status

approved