  In this paper we give simple expressions, involving binomials coefficients,
for the value of $c(n,k)$ modulo $p^{v_p(n)}$, when $v_p(n) > 0$. Here $c(n,k)$
denotes a Stirling number of the first kind, and $v_p(n)$ is the highest power
of $p$ dividing $n$.
  As an application, we compute the Chern classes of permutation
representations of cyclic groups.
