On certain inequalities about arithmetic functions which use the exponential divisors (Q2907099)

A positive integer \(d=\prod_{i=1}^r p_i^{b_i}\) is said to be an exponential divisor of \(n=\prod_{i=1}^r p_i^{a_i}\) if \(b_i\) divides \(a_i\) for every \(i=1, 2,\dots, r\), see \textit{M. V. Subbarao} [Lect. Notes Math. 251, 247--271 (1972; Zbl 0237.10009)].NEWLINENEWLINEThe present author proves various inequalities for the number, sum and product of exponential divisors functions. He also shows that if \(n\) is exponentially perfect, then at least one exponent \(a_i\) is equal to \(2\). For a survey of exponentially perfect numbers see \textit{J. Sándor} and \textit{B. Crstici} [Handbook of Number Theory. II. Dordrecht: Kluwer (2004; Zbl 1079.11001)].