A339481 a(n) = Sum_{d|n} d^(n-d) * binomial(d+n/d-2, d-1).

1, 2, 2, 10, 2, 131, 2, 1282, 4376, 16907, 2, 1138272, 2, 5793475, 154455992, 469893122, 2, 49501130330, 2, 1318441711177, 19001093813466, 3138439911059, 2, 15989399214596398, 6675720214843752, 3937376603803099, 6754271297694102092, 47097064577536888014, 2

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Formula

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

If p is prime, a(p) = 2.

Mathematica

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

Prog

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

Crossrefs

Cf. A157019, A157020, A324158, A324159, A338661, A339482, A339712, A343573.

Sequence in context: A321415 A319692 A308693 * A163937 A083457 A163808

Adjacent sequences: A339478 A339479 A339480 * A339482 A339483 A339484

Keyword

nonn

Author

Seiichi Manyama, Apr 24 2021

Status

approved