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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

Marius A. Burtea, Table of n, a(n) for n = 6..5000

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

Cf. A000741, A000742, A000743, A023032, A023033, A023034, A023035.

Sequence in context: A306940 A120478 A008488 * A090581 A000389 A143980

Adjacent sequences:  A023028 A023029 A023030 * A023032 A023033 A023034

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified August 13 00:27 EDT 2020. Contains 336441 sequences. (Running on oeis4.)