  Let $d \ge 3$ be an integer and let $P \in \mathbb{Z}[x]$ be a polynomial of
degree $d$ whose Galois group is $S_d$. Let $(a_n)$ be a linearly recuresive
sequence of integers which has $P$ as its characteristic polynomial. We prove,
under the generalized Riemann hypothesis, that the lower density of the set of
primes which divide at least one element of the sequence $(a_n)$ is positive.
