On certain arithmetic functions involving exponential divisors

Abstract

The integer $d$ is called an exponential divisor of $n={\prod }_{i=1}^r{p}_i^{a_i}>1$ if $d={\prod }_{i=1}^r{p}_i^{c_i}$, where $c_i\mid a_i$ for every $1\le i\le r$. The integers $n={\prod }_{i=1}^r{p}_i^{a_i},m={\prod }_{i=1}^r{p}_i^{b_i}>1$ having the same prime factors are called exponentially coprime if $(a_i,b_i)=1$ for every $1\le i\le r$. In the paper we investigate asymptotic properties of certain arithmetic functions involving exponential divisors and exponentially coprime integers.

some misprints corrected

References in corpus (1)

• The maximal order of a class of multiplicative arithmetical functions