%I #23 Sep 08 2022 08:44:47
%S 1,7,28,84,210,462,924,1715,3003,4998,8008,12348,18564,27048,38759,
%T 54054,74613,100478,134596,176176,230202,294294,376740,471933,593775,
%U 731276,905982,1099560,1344903,1610322,1947792,2306220,2759757,3235484,3838380
%N Number of compositions of n into 7 ordered relatively prime parts.
%H Marius A. Burtea, <a href="/A023032/b023032.txt">Table of n, a(n) for n = 7..5000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Moebius transform of C(n-1,6).
%F G.f.: Sum_{k>=1} mu(k) * x^(7*k) / (1 - x^k)^7. - _Ilya Gutkovskiy_, Feb 05 2020
%p with(numtheory):
%p a:= n-> add(mobius(n/d)*binomial(d-1, 6), d=divisors(n)):
%p seq(a(n), n=7..50); # _Alois P. Heinz_, Feb 05 2020
%t 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 *)
%o (Magma) [&+[MoebiusMu(n div d)*Binomial(d-1,6):d in Divisors(n)]:n in[7..41]]; // _Marius A. Burtea_, Feb 07 2020
%Y Cf. A000741, A000742, A000743, A023031, A023033, A023034, A023035.
%K nonn
%O 7,2
%A _David W. Wilson_