A338657 a(n) = Sum_{d|n} mu(d) * binomial(d+n/d-1, d).
1, 1, 2, 1, 4, -3, 6, -2, -1, -10, 10, -22, 12, -21, -40, -20, 16, -55, 18, -80, -98, -55, 22, -90, -101, -78, -138, -182, 28, -271, 30, -104, -330, -136, -756, -37, 36, -171, -520, -676, 40, -476, 42, -550, -1786, -253, 46, 648, -1667, -1276, -1088, -832, 52, 1539, -4312
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
a[n_] := DivisorSum[n, MoebiusMu[#] * Binomial[# + n/# - 1, #] &]; Array[a, 100] (* Amiram Eldar, Apr 22 2021 *)
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PARI
a(n) = sumdiv(n, d, moebius(d)*binomial(d+n/d-1, d));
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PARI
my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, moebius(k)*x^k/(1-x^k)^(k+1)))
Formula
G.f.: Sum_{k >= 1} mu(k) * x^k/(1 - x^k)^(k+1).
If p is prime, a(p) = p - 1.