%I #6 Sep 14 2021 08:56:28
%S 1,1,1,1,2,3,5,6,10,16,19,31,44,52,86,101,148,206,237,350,441,551,743,
%T 900,1151,1470,1782,2216,2762,3287,4072,4894,5835,7052,8362,9856,
%U 11758,13710,16066,18791,21799,25271,29192,33583,38485,44178,50304
%N Number of compositions (ordered partitions) of n into at most 6 nonprime parts.
%t Table[Length@Flatten[Permutations/@IntegerPartitions[n,6,Select[Range@n,!PrimeQ@#&]],1],{n,0,46}] (* _Giorgos Kalogeropoulos_, Sep 14 2021 *)
%Y Cf. A018252, A052284, A341483, A347788, A347796, A347797, A347798.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Sep 14 2021