Arithmetic Functions Associated with Exponentially Odd and Exponentially Even Integers

Annual Meeting in Mathematics 2023

Abstract

An exponentially even integer is a positive integer whose prime factorization contains only even prime powers, while an exponentially odd integer is a positive integer whose prime factorization contains only odd prime powers. We investigate here the problem of counting the number of positive integers that are semi-prime to an exponentially even integer, and to an exponentially odd integer. Basic properties of the functions involved are established.