  This paper provides a mean value theorem for arithmetic functions $f$ defined
by $$f(n)=\prod_{d|n}g(d),$$ where $g$ is an arithmetic function taking values
in $(0, 1]$ and satisfying some generic conditions. As an application of our
main result, we prove that the density $\mu_q(n)$ (resp. $\rho_q(n)$) of normal
(resp. primitive) elements in the finite field extension $\mathbb{F}_{q^n}$ of
$\mathbb{F}_q$ are arithmetic functions of (non zero) mean values.
