Exponential unitary divisors

Abstract. We say that \(d\) is an exponential unitary divisor of \(n=p_1^{a_1}\cdots p_r^{a_r}>1\) if \(d=p_1^{b_1}\cdots p_r^{b_r}\), 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 \(i\in \{1,2,\ldots,r\}\). We survey properties of related arithmetical functions and introduce the notion of exponential unitary perfect numbers.