On the Parity of p(n,3) and p_Ψ(n,3)

A partition of $n$ is \emph{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 $p_{\Psi}(n,k)$. In this paper we deal with the parities of $p(n,3)$ and $p_{\Psi}(n,3)$