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%I #10 Oct 03 2021 15:37:37
%S 1,1,2,4,6,9,10,12,13,15,15,16,13,18,17,24,19,25,18,30,24,36,23,37,23,
%T 44,29,45,19,43,20,54,30,54,25,60,29,67,29,60,21,70,28,78,38,77,31,88,
%U 33,95,44,91,30,100,30,110,42,97,25,109,35,129,49,113,31,135
%N Number of compositions (ordered partitions) of n into at most 3 noncomposite parts.
%C "Noncomposite" means "1 or a prime".
%t Table[Length@Flatten[Permutations/@IntegerPartitions[n,3,Join[{1},Prime@Range@PrimePi@n]],1],{n,0,65}] (* _Giorgos Kalogeropoulos_, Sep 12 2021 *)
%Y Cf. A008578, A280917, A283762, A347740, A347744.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 11 2021