Vol. 52, No. 1, 1974

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On the distribution of numbers of the form σ(n)∕n and on some related questions

Paul Erdős

Vol. 52 (1974), No. 1, 59–65
Abstract

A number theoretic function f(n) is called multiplicative if f(ab) = f(a)f(b) for (a,b) = 1, it is called additive if f(ab) = f(a) + f(b) for (a,b) = 1. A function f(n) is said to have a distribution function if for every c the density g(c) of integers satisfying f(n) < c exists and g(−∞) = 0,g() = 1. In this note we give some best possible estimates for g(c + 1∕t) g(t), for the case of f(n) = σ(n)∕n.

Mathematical Subject Classification
Primary: 10K20
Milestones
Received: 30 January 1973
Published: 1 May 1974
Authors
Paul Erdős