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A023032
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Number of compositions of n into 7 ordered relatively prime parts.
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10
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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
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OFFSET
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7,2
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LINKS
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FORMULA
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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
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MAPLE
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with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 6), d=divisors(n)):
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MATHEMATICA
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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 *)
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PROG
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(Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 6):d in Divisors(n)]:n in[7..41]]; // Marius A. Burtea, Feb 07 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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