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).
Mohamed El Bachraoui (Wed,) studied this question.