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

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.

number theory, mosaic, factorization
Mathematical Subject Classification 2000
Primary: 11A99, 11A25, 11A05
Received: 8 February 2008
Accepted: 20 July 2008
Published: 18 March 2009

Communicated by Andrew Granville
Kristen Bildhauser
Saint Mary’s College
Notre Dame, IN 46556
United States
Jared Erickson
School of Engineering and Applied Science
Northwestern University
2145 Sheridan Road Room C210
Evanston, IL 60208
United States
Cara Tacoma
Trinity Christian College
Palos Heights, IL 60463
United States
Rick Gillman
Valparaiso University
Valparaiso, IN 46383
United States