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Number of compositions (ordered partitions) of n into at most 6 prime powers (including 1).
1

%I #6 Sep 13 2021 11:37:27

%S 1,1,2,4,8,16,31,61,115,207,353,572,882,1305,1863,2581,3491,4615,5974,

%T 7583,9462,11616,14070,16844,19965,23436,27289,31502,36104,41074,

%U 46462,52244,58534,65230,72458,80118,88352,97011,106448,116393,127189,138532,150819,163473

%N Number of compositions (ordered partitions) of n into at most 6 prime powers (including 1).

%t Table[Length@Flatten[Permutations/@IntegerPartitions[n,6,Join[{1},Select[Range@n,PrimePowerQ]]],1],{n,0,43}] (* _Giorgos Kalogeropoulos_, Sep 13 2021 *)

%Y Cf. A000961, A280543, A341135, A347762, A347763, A347764, A347775.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Sep 13 2021