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%I #24 Sep 08 2022 08:44:47
%S 1,10,55,220,715,2002,5005,11440,24310,48620,92377,167960,293920,
%T 497420,817135,1307504,2042755,3124550,4686110,6906900,10013002,
%U 14307150,20155070,28048790,38555660,52451256,70583095,94143280,124355000
%N Number of compositions of n into 10 ordered relatively prime parts.
%H Marius A. Burtea, <a href="/A023035/b023035.txt">Table of n, a(n) for n = 10..5000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Moebius transform of C(n-1,9).
%F G.f.: Sum_{k>=1} mu(k) * x^(10*k) / (1 - x^k)^10. - _Ilya Gutkovskiy_, Feb 05 2020
%p with(numtheory):
%p a:= n-> add(mobius(n/d)*binomial(d-1, 9), d=divisors(n)):
%p seq(a(n), n=10..50); # _Alois P. Heinz_, Feb 05 2020
%t a[n_]:=Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k -1, 9], {k, 1, n}]; Table[a[n], {n, 10, 45}] (* or *) Table[a[n],{n, 9, 45}] a[n_]:=DivisorSum[n, Binomial[#-1,9] MoebiusMu[n/#]&]; Array[a, 37, 10] (* _Vincenzo Librandi_, Feb 08 2020 *)
%o (Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 9):d in Divisors(n)]:n in[10..42]]; // _Marius A. Burtea_, Feb 07 2020
%Y Cf. A000741, A000742, A000743, A023031, A023032, A023033, A023034.
%Y Cf. A023023, A023024, A023025, A023026, A023027, A023028, A023029, A023030.
%K nonn
%O 10,2
%A _David W. Wilson_
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