A023032 Number of compositions of n into 7 ordered relatively prime parts.

1, 7, 28, 84, 210, 462, 924, 1715, 3003, 4998, 8008, 12348, 18564, 27048, 38759, 54054, 74613, 100478, 134596, 176176, 230202, 294294, 376740, 471933, 593775, 731276, 905982, 1099560, 1344903, 1610322, 1947792, 2306220, 2759757, 3235484, 3838380

Offset

7,2

Links

Marius A. Burtea, Table of n, a(n) for n = 7..5000

N. J. A. Sloane, Transforms

Formula

Moebius transform of C(n-1,6).

G.f.: Sum_{k>=1} mu(k) * x^(7*k) / (1 - x^k)^7. - Ilya Gutkovskiy, Feb 05 2020

Maple

with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 6), d=divisors(n)):
seq(a(n), n=7..50);  # Alois P. Heinz, Feb 05 2020

Mathematica

a[n_]:=DivisorSum[n, Binomial[#-1, 6] MoebiusMu[n/#]&]; Array[a, 37, 7] (* or *) a[n_]:=Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k-1, 6], {k, 1, n}]; Table[a[n], {n, 7, 45}] (* Vincenzo Librandi, Feb 07 2020 *)

Prog

(Magma)  [&+[MoebiusMu(n div d)*Binomial(d-1, 6):d in Divisors(n)]:n in[7..41]]; // Marius A. Burtea, Feb 07 2020

Crossrefs

Cf. A000741, A000742, A000743, A023031, A023033, A023034, A023035.

Sequence in context: A375163 A049018 A008489 * A341204 A278969 A000579

Adjacent sequences: A023029 A023030 A023031 * A023033 A023034 A023035

Keyword

nonn

Author

David W. Wilson

Status

approved