Experimental Mathematics

Bounds for the density of abundant integers

Marc Deléglise

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 [wall71] 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 $0.2474 < A(2) < 0.2480$.

Article information

Source
Experiment. Math. Volume 7, Issue 2 (1998), 137-143.

Dates
First available in Project Euclid: 24 March 2003

Permanent link to this document
http://projecteuclid.org/euclid.em/1048515661

Mathematical Reviews number (MathSciNet)
MR1677091

Zentralblatt MATH identifier
0923.11127

Subjects
Primary: 11N60: Distribution functions associated with additive and positive multiplicative functions

Citation

Deléglise, Marc. Bounds for the density of abundant integers. Experiment. Math. 7 (1998), no. 2, 137--143. http://projecteuclid.org/euclid.em/1048515661.


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