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A023031
Number of compositions of n into 6 ordered relatively prime parts.
10
1, 6, 21, 56, 126, 252, 461, 792, 1281, 2002, 2982, 4368, 6131, 8568, 11502, 15498, 20097, 26334, 33166, 42504, 52338, 65724, 79443, 98280, 116626, 142506, 166908, 201124, 232968, 278250, 317983, 376992, 427329, 501150, 564108, 658008, 732612
OFFSET
6,2
LINKS
N. J. A. Sloane, Transforms
FORMULA
Moebius transform of C(n-1,5).
G.f.: Sum_{k>=1} mu(k) * x^(6*k) / (1 - x^k)^6. - Ilya Gutkovskiy, Feb 05 2020
MAPLE
with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 5), d=divisors(n)):
seq(a(n), n=6..50); # Alois P. Heinz, Feb 05 2020
MATHEMATICA
a[n_]:=DivisorSum[n, Binomial[#-1, 5] MoebiusMu[n/#]&]; Array[a, 37, 6] (* or *) a[n_]:=Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k - 1, 5], {k, 1, n}]; Table[a[n], {n, 6, 45}] (* Vincenzo Librandi, Feb 06 2020 *)
PROG
(Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 5):d in Divisors(n)]:n in[6..42]]; // Marius A. Burtea, Feb 07 2020
KEYWORD
nonn
STATUS
approved