  The Smarandache function of a positive integer $n$, denoted by $S(n)$, is
defined to be the smallest positive integer $j$ such that $n$ divides the
factorial $j!$. In this note, we prove that for any fixed number $k > 1$, the
inequality $n^k < S(n)!$ holds for almost all positive integers $n$. This
confirms Sondow's conjecture which asserts that the inequality $n^2 < S(n)!$
holds for almost all positive integers $n$.
