SCHWEITZER 1985 Problem 4

Call a subset $S$ of the set $\{1,\dots,n\}$ exceptional if any pair of distinct elements of $S$ are coprime. Consider an exceptional set with a maximal sum of elements (among all exceptional sets for a fixed $n$ ). Prove that if $n$ is sufficiently large, then each element of $S$ has at most two distinct prime divisors. (N.17) [P. Erdos]