Previous work showed that, for ν 2 (n) the number of partitions of n into exactly two part sizes, one has ν 2 (16n + 14) 蠁 0 (mod 4). The earlier proof required the technology of modular forms, and a combinatorial proof was desired. This article provides the requested proof, in the process refining divisibility to finer subclasses. Some of these subclasses have counts closely related to the divisor function d(16n + 14), and we offer a conjecture on a potential rank statistic
DeWitt et al. (Thu,) studied this question.