%I #28 Sep 08 2022 08:44:47

%S 1,6,21,56,126,252,461,792,1281,2002,2982,4368,6131,8568,11502,15498,

%T 20097,26334,33166,42504,52338,65724,79443,98280,116626,142506,166908,

%U 201124,232968,278250,317983,376992,427329,501150,564108,658008,732612

%N Number of compositions of n into 6 ordered relatively prime parts.

%H Marius A. Burtea, <a href="/A023031/b023031.txt">Table of n, a(n) for n = 6..5000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F Moebius transform of C(n-1,5).

%F G.f.: Sum_{k>=1} mu(k) * x^(6*k) / (1 - x^k)^6. - _Ilya Gutkovskiy_, Feb 05 2020

%p with(numtheory):

%p a:= n-> add(mobius(n/d)*binomial(d-1, 5), d=divisors(n)):

%p seq(a(n), n=6..50); # _Alois P. Heinz_, Feb 05 2020

%t 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 *)

%o (Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 5):d in Divisors(n)]:n in[6..42]]; // _Marius A. Burtea_, Feb 07 2020

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

%K nonn

%O 6,2

%A _David W. Wilson_