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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 (list; graph; refs; listen; history; text; internal format)
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
CROSSREFS
Sequence in context: A306940 A120478 A008488 * A341203 A090581 A000389
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)