On divisors of odd perfect numbers

Abstract

A perfect number is a positive integer the sum of whose divisors is equal to twice the number itself. Twenty-three even perfect numbers have been discovered to date [2]. No odd perfect number has yet been found, but various restrictions which an odd perfect number must satisfy have been established. For a summary, see [7]. For a perfect number n, a(n) = 2n, where a(n) denotes the sum of the divisors of n. Let