Date of Graduation

Fall 2018

Document Type

Honors Research Project

Degree Name

Bachelor of Science

Major

Mathematics

Research Sponsor

Dr. Jeffrey Riedl

First Reader

Dr. James Cossey

Second Reader

Dr. Stefan Forcey

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.

Comments

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

Included in

Number Theory Commons

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