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%I #7 Sep 12 2021 20:35:40
%S 1,1,2,4,7,11,15,20,24,29,34,40,45,52,55,58,62,67,69,76,79,87,88,92,
%T 89,100,96,106,109,121,111,127,125,140,139,158,149,173,152,168,159,
%U 184,156,196,168,193,173,206,173,220,186,222,201,236,185,243,203,252
%N Number of compositions (ordered partitions) of n into at most 3 prime powers (including 1).
%t Table[Length@Flatten[Permutations/@IntegerPartitions[n,3,Join[{1},Select[Range@n,PrimePowerQ]]],1],{n,0,70}] (* _Giorgos Kalogeropoulos_, Sep 12 2021 *)
%Y Cf. A000961, A280543, A282064, A347762, A347764.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 12 2021