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

Positive lower density for prime divisors of generic linear recurrences