An algorithm to determine all odd primitive abundant numbers with d prime divisors

Author

Jacob LiddyFollow

Date of Last Revision

2023-05-03 05:05:06

Major

Mathematics

Degree Name

Bachelor of Science

Date of Expected Graduation

Fall 2018

Abstract

An abundant number is said to be primitive if none of its proper divisors are abundant. Dickson proved that for an arbitrary positive integer d there exists only finitely many odd primitive abundant numbers having exactly d prime divisors. In this paper we describe a fast algorithm that finds all primitive odd numbers with d unique prime divisors. We use this algorithm to find all the number of odd primitive abundant numbers with 6 unique Divisors. We use this algorithm to prove that an odd weird number must have at least 6 prime divisors.

Research Sponsor

Dr. Jeffrey Riedl

First Reader

Dr. James Cossey

Second Reader

Dr. Stefan Forcey

Comments

Finding the exact OPAN(6) Is currently in progress on a server.

Recommended Citation

Liddy, Jacob, "An algorithm to determine all odd primitive abundant numbers with d prime divisors" (2018). Williams Honors College, Honors Research Projects. 728.
https://ideaexchange.uakron.edu/honors_research_projects/728