A344777 a(n) = Sum_{d|n} (-1)^(n/d-1) * binomial(d+n/d-1, d).

1, -1, 4, -6, 6, -3, 8, -22, 20, 0, 12, -44, 14, 7, 72, -95, 18, -10, 20, -71, 142, 33, 24, -399, 152, 52, 248, -57, 30, -121, 32, -679, 398, 102, 828, -685, 38, 133, 600, -1568, 42, -140, 44, 318, 2864, 207, 48, -5858, 1766, -751, 1192, 831, 54, 348, 4424, -3979, 1598, 348, 60

Offset

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, (-1)^(n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 60] (* Amiram Eldar, May 28 2021 *)

Prog

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

Crossrefs

Cf. A081543, A217670, A338682.

Sequence in context: A019923 A019800 A349701 * A191761 A201451 A200352

Adjacent sequences: A344774 A344775 A344776 * A344778 A344779 A344780

Keyword

sign

Author

Seiichi Manyama, May 28 2021

Status

approved