On the Parity of p(n,3) and p_Ψ(n,3)

A partition of n is relatively prime if its parts form a relatively prime set. The number of partitions of n into exactly k parts is denoted by p(n,k) and the number of relatively prime partitions into exactly k parts is denoted by pΨ(n,k). In this paper we deal with the parities of p(n,3) and pΨ(n,3).