How to find Integers that Cannot Divide Odd Perfect Numbers using a Generalization of Sylvester's Proof

A widely known and thought about open question in number theory is whether or not an odd perfect number, that is an odd positive integer equal to the sum of its proper divisors, exists. In 1888, James Joseph Sylvester proved that such a number cannot be divisible by 105. This presentation includes an extension of Sylvester's proof discovered recently by the speaker and lists more integers that can be proven not to divide an odd perfect number. We will also discuss how to find such integers.