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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513799117

Digital Object Identifier
doi:10.2140/involve.2009.2.65

Mathematical Reviews number (MathSciNet)
MR2501345

Zentralblatt MATH identifier
1225.11007

Subjects
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

Keywords
number theory mosaic factorization

Citation

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. https://projecteuclid.org/euclid.involve/1513799117


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References

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