Cool Subsets

An integer $X$ is *cool* if it has a primitive root modulo $X$. The *coolness* of a non-empty set of $N$ distinct integers $S = \{x_1, x_2, \ldots, x_N\}$ is the number of cool divisors of $\prod_{i=1}^N x_i$. You are given four integers $L$, $R$, $A$ and $B$. Let $S$ be the set containing all integers between $L$ and $R$ (inclusive). Consider all non-empty subsets of $S$ with size between $A$ a