Putnam 2017 A1

Let $S$ be the smallest set of positive integers such that

(a) $2$ is in $S$,

(b) $n$ is in $S$ whenever $n^2$ is in $S$, and

(c) $(n+5)^2$ is in $S$ whenever $n$ is in $S$.

Which positive integers are not in $S$?

(The set $S$ is "smallest" in the sense that $S$ is contained in any other such set.)