Exponential unitary divisors

Abstract

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.

8 pages

References in corpus (1)

• The ring of arithmetical functions with unitary convolution: Divisorial and topological properties

Cited by in corpus (1)

• Conditional Results for a Class of Arithmetic Functions: a variant of H. L. Montgomery and R. C. Vaughan's method