A339482 a(n) = Sum_{d|n} d^(n-d+1) * binomial(d+n/d-2, d-1).

1, 3, 4, 21, 6, 346, 8, 4617, 13132, 80696, 12, 4903847, 14, 40410966, 756336736, 2416181265, 18, 306560794753, 20, 6941876836216, 132964265599502, 34522735212626, 24, 116720277621236637, 33378601074218776, 51185893450298400, 60788365423272068968

Offset

1,2

Links

Table of n, a(n) for n=1..27.

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, #^(n - # + 1) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 30] (* Amiram Eldar, Apr 25 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(n-d+1)*binomial(d+n/d-2, d-1));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k*(x/(1-(k*x)^k))^k))

Crossrefs

Cf. A157019, A157020, A324158, A324159, A338661, A339481, A339712, A343573.

Sequence in context: A206032 A197410 A308689 * A359883 A032830 A225478

Adjacent sequences: A339479 A339480 A339481 * A339483 A339484 A339485

Keyword

nonn

Author

Seiichi Manyama, Apr 24 2021

Status

approved