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A023033
Number of compositions of n into 8 ordered relatively prime parts.
9
1, 8, 36, 120, 330, 792, 1716, 3432, 6434, 11440, 19440, 31824, 50352, 77520, 116160, 170544, 244826, 346104, 479908, 657792, 886314, 1184040, 1557312, 2035800, 2623140, 3365736, 4260608, 5379616, 6704742, 8347680, 10263648, 12619464
OFFSET
8,2
LINKS
N. J. A. Sloane, Transforms
FORMULA
Moebius transform of C(n-1,7).
G.f.: Sum_{k>=1} mu(k) * x^(8*k) / (1 - x^k)^8. - Ilya Gutkovskiy, Feb 05 2020
MAPLE
with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 7), d=divisors(n)):
seq(a(n), n=8..50); # Alois P. Heinz, Feb 05 2020
MATHEMATICA
a[n_]:=DivisorSum[n, Binomial[# - 1, 7] MoebiusMu[n/#]&]; Array[a, 37, 8] (* or *) a[n_]:=Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k - 1, 7], {k, 1, n}]; Table[a[n], {n, 8, 45}] (* Vincenzo Librandi, Feb 07 2020 *)
PROG
(Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 7):d in Divisors(n)]:n in[8..40]]; // Marius A. Burtea, Feb 07 2020
KEYWORD
nonn
STATUS
approved