On the Sum and Product of Distinct Prime Factors of an Odd Perfect Number

TL;DR

This paper establishes lower bounds on the sum and product of distinct prime factors of odd perfect numbers, linking these bounds to the overall size of such numbers based on their prime factorization.

Contribution

It introduces new lower bounds on prime factors of odd perfect numbers, connecting prime factorization properties to the number's size.

Findings

Lower bounds on the sum of prime factors.

Lower bounds on the product of prime factors.

A relationship between prime factors and the size of odd perfect numbers.

Abstract

We present lower bounds on the sum and product of the distinct prime factors of an odd perfect number, which provide a lower bound on the size of the odd perfect number as a function of the number of its distinct prime factors.