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%I #7 Sep 13 2021 11:37:13
%S 1,1,2,4,8,16,30,55,94,151,227,326,450,603,786,1005,1259,1543,1856,
%T 2201,2571,2978,3417,3896,4402,4950,5506,6104,6710,7366,8040,8792,
%U 9526,10342,11150,12042,12918,13977,14975,16145,17242,18514,19628,21015,22170,23671,24940
%N Number of compositions (ordered partitions) of n into at most 5 prime powers (including 1).
%t Table[Length@Flatten[Permutations/@IntegerPartitions[n,5,Join[{1},Select[Range@n,PrimePowerQ]]],1],{n,0,46}] (* _Giorgos Kalogeropoulos_, Sep 13 2021 *)
%Y Cf. A000961, A280543, A341134, A347762, A347763, A347764, A347776.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 13 2021