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Number of compositions (ordered partitions) of n into at most 5 nonprime parts.
4

%I #7 Sep 14 2021 08:56:23

%S 1,1,1,1,2,3,4,6,10,10,19,25,29,46,50,75,103,110,162,194,240,309,368,

%T 444,565,654,795,960,1106,1325,1560,1792,2118,2436,2785,3244,3691,

%U 4194,4783,5419,6121,6893,7780,8617,9766,10790,12060,13340,14851,16231,18210

%N Number of compositions (ordered partitions) of n into at most 5 nonprime parts.

%t Table[Length@Flatten[Permutations/@IntegerPartitions[n,5,Select[Range@n,!PrimeQ@#&]],1],{n,0,50}] (* _Giorgos Kalogeropoulos_, Sep 14 2021 *)

%Y Cf. A018252, A052284, A341482, A347788, A347796, A347797, A347799.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Sep 14 2021