Date

2019

Department or Program

Mathematics

Primary Wellesley Thesis Advisor

Alex Diesl

Abstract

If we let S(n) be the sum of the prime factors (with multiplicity) of an integer n, then we define a Ruth-Aaron Number to be any n such that S(n)=S(n+1). The main results regarding Ruth-Aaron numbers that Erdos and Pomerance proved show that the Ruth-Aaron numbers have density zero and the sum of their reciprocals converges. We extend their results by replacing the function S (which sums the prime powers of a number n) with other functions f on the prime factors. In the process we take a look at the history of analytic number theory, and review some classical results from the field.

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