  Let $\rho(n)$ denote the maximal number of different primes that may occur in
the order of a finite solvable group $G$, all elements of which have orders
divisible by at most $n$ distinct primes. We show that $\rho(n)\leq 5n$ for all
$n\geq 1$. As an application, we improve on a recent bound by Hung and Yang for
arbitrary finite groups.
