Bounds for the density of abundant integers. (English) Zbl 0923.11127

An integer \(n\) is called abundant if the sum of the divisors of \(n\) is at least \(2n\). It is known that abundant numbers have natural density \(d\) and that \(0.244<d<0.291\). The author answers a question by H. Cohen, showing that \(d<1/4\). Precisely, using a method of Behrend the authors shows that \(0.2474<d<0.2480\).


11N25 Distribution of integers with specified multiplicative constraints
11A25 Arithmetic functions; related numbers; inversion formulas
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