Vol. 2, No. 1, 2009

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Divisor concepts for mosaics of integers

Kristen Bildhauser, Jared Erickson, Cara Tacoma and Rick Gillman

Vol. 2 (2009), No. 1, 65–78
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.

Keywords
number theory, mosaic, factorization
Mathematical Subject Classification 2000
Primary: 11A99, 11A25, 11A05