Involve: A Journal of Mathematics

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

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.

Article information

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

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

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

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

References

• R. A. Gillman, “Some new functions on the mosaic of $n$”, J. Natur. Sci. Math. 30:1 (1990), 47–56.
• R. A. Gillman, “$k$-distributive functions on the mosaic of $n$”, J. Nat. Sci. Math. 32 (1992), 25–29.
• A. A. Mullin, “On a final multiplicative formulation of the fundamental theorem of arithmetic”, Z. Math. Logik Grundlagen Math. 10 (1964), 159–161.
• A. A. Mullin, “A contribution toward computable number theory”, Z. Math. Logik Grundlagen Math. 11 (1965), 117–119.
• A. A. Mullin, “On Möbius' function and related matters”, Amer. Math. Monthly 74 (1967), 1100–1102.
• A. A. Mullin, “On new theorems for elementary number theory”, Notre Dame J. Formal Logic 8 (1967), 353–356.