Let $S:=\{x_1,x_2,\dots,x_n\}$ be a finite set of natural numbers. Is there an efficient algorithm to find how many numbers divide at least one of $x_i$ in the set $S$?
For example. If $S=\{2,6,15\}$ then the divisors of each of the members are:
$\begin{array}{rl} 2: & \{1, 2\} \\ 6: & \{1, 2, 3, 6\} \\ 15:& \{1, 3, 5, 15\} \\ \end{array}$
If we take the union of the divisor sets, we get $\{1, 2, 3, 5, 6, 15\}$, which has $6$ elements, so the answer is $6$.