Bounds for the Density of Abundant Integers

Abstract

We say that an integer n is abundant if the sum of the divisors of n is at least 2n. It has been known (Wall 1972] that the set of abundant numbers has a natural density A(2) and that 0.244 < A(2) < 0.291. We give the sharper bounds 0.2474 < A(2) < 0.2480.