Divisor concepts for mosaics of integers

Abstract

The mosaic of the integer $n$ is the array of prime numbers resulting from iterating the Fundamental Theorem of Arithmetic on $n$ and on any resulting composite exponents. In this paper, we generalize several number theoretic functions to the mosaic of $n$, first based on the primes of the mosaic, second by examining several possible definitions of a divisor in terms of mosaics. Having done so, we examine properties of these functions.