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

8,2

Links

Marius A. Burtea, Table of n, a(n) for n = 8..5000

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

Crossrefs

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

Sequence in context: A008500 A306941 A008490 * A341205 A278971 A000580

Adjacent sequences: A023030 A023031 A023032 * A023034 A023035 A023036

Keyword

nonn

Author

David W. Wilson

Status

approved