A347739 Number of compositions (ordered partitions) of n into at most 2 prime parts.

1, 0, 1, 1, 1, 3, 1, 3, 2, 2, 3, 1, 2, 3, 3, 2, 4, 1, 4, 3, 4, 2, 5, 1, 6, 2, 5, 0, 4, 1, 6, 3, 4, 2, 7, 0, 8, 1, 3, 2, 6, 1, 8, 3, 6, 2, 7, 1, 10, 2, 8, 0, 6, 1, 10, 2, 6, 0, 7, 1, 12, 3, 5, 2, 10, 0, 12, 1, 4, 2, 10, 1, 12, 3, 9, 2, 10, 0, 14, 1, 8

Offset: 0

Author

Ilya Gutkovskiy, Sep 11 2021

Keywords

• nonn

Crossrefs

Cf. A000040, A023360, A073610, A121303, A347740, A347741, A347742, A347743.

Programs

Mathematica

Table[Length@Flatten[Permutations/@IntegerPartitions[n,2,Prime@Range@PrimePi@n],1],{n,0,100}] (* Giorgos Kalogeropoulos, Sep 12 2021 *)

Formula

a(n) = Sum_{k=1..2} A121303(n,k) for n >= 2. - Alois P. Heinz, Sep 11 2021