Exponential unitary divisors

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$b_i$isaunitarydivisorof$a_i$,i\mathrm{.}e\mathrm{.},$b_i\mid a_i$and$(b_i,a_i/b_i)=1$forevery$i\in {1,2,…,r}$. We survey properties of related arithmetical functions and introduce the notion of exponential unitary perfect numbers.