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A023032 Number of compositions of n into 7 ordered relatively prime parts. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A008499 A049018 A008489 * A278969 A000579 A290994

Adjacent sequences:  A023029 A023030 A023031 * A023033 A023034 A023035

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.)