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Original Articles

Bounds for the Density of Abundant Integers

Pages 137-143 | Published online: 03 Apr 2012
 

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.

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