  We say that $d$ is an exponential unitary divisor of $n=p_1^{a_1}...
p_r^{a_r}>1$ if $d=p_1^{b_1}... p_r^{b_r}$, where $b_i$ is a unitary divisor of
$a_i$, i.e., $b_i\mid a_i$ and $(b_i,a_i/b_i)=1$ for every $i\in
\{1,2,...,r\}$. We survey properties of related arithmetical functions and
introduce the notion of exponential unitary perfect numbers.
