Involve: A Journal of Mathematics

  • Involve
  • Volume 2, Number 1 (2009), 65-78.

Divisor concepts for mosaics of integers

Kristen Bildhauser, Jared Erickson, Cara Tacoma, and Rick Gillman

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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.

Article information

Involve, Volume 2, Number 1 (2009), 65-78.

Received: 8 February 2008
Accepted: 20 July 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11A99: None of the above, but in this section 11A25: Arithmetic functions; related numbers; inversion formulas 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors

number theory mosaic factorization


Bildhauser, Kristen; Erickson, Jared; Tacoma, Cara; Gillman, Rick. Divisor concepts for mosaics of integers. Involve 2 (2009), no. 1, 65--78. doi:10.2140/involve.2009.2.65.

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