The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #6 Sep 12 2021 20:35:29
%S 1,1,2,4,7,14,26,49,87,143,220,316,435,576,739,911,1100,1297,1541,
%T 1798,2113,2405,2785,3136,3648,4061,4670,5080,5828,6301,7261,7692,
%U 8751,9059,10379,10681,12329,12435,14354,14335,16847,16673,19588,18866,22247,21257
%N Number of compositions (ordered partitions) of n into at most 6 prime parts (counting 1 as a prime).
%t Table[Length@Flatten[Permutations/@IntegerPartitions[n,6,Join[{1},Prime@Range@PrimePi@n]],1],{n,0,45}] (* _Giorgos Kalogeropoulos_, Sep 12 2021 *)
%Y Cf. A008578, A280917, A341985, A347703, A347743, A347744, A347745, A347760.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 12 2021