A338688 - OEIS

A338688

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

1, 1, 4, -5, 6, 2, 8, -121, 172, 44, 12, -759, 14, 566, 5536, -7665, 18, -6877, 20, 2744, 70862, 21218, 24, -570573, 218776, 104324, 918568, 942479, 30, -3693495, 32, -9408481, 11779582, 2223344, 19935756, -15628120, 38, 9954650, 145283360, -371959011, 42, -382916059

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..42.

FORMULA

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

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

MATHEMATICA

a[n_] := -DivisorSum[n, (-n/#)^# * Binomial[# + n/# - 2, # - 1] &]; Array[a, 40] (* Amiram Eldar, Apr 24 2021 *)

PROG

(PARI) a(n) = -sumdiv(n, d, (-n/d)^d*binomial(d+n/d-2, d-1));