A023033 Number of compositions of n into 8 ordered relatively prime parts.

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

Author

David W. Wilson

Keywords

• nonn

Links

• Marius A. Burtea, Table of n, a(n) for n = 8..5000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000741, A000742, A000743, A023031, A023032, A023034, A023035.

Programs

Magma

[&+[MoebiusMu(n div d)*Binomial(d-1,7):d in Divisors(n)]:n in[8..40]]; // Marius A. Burtea, Feb 07 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 *)

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