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

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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(a b) = 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.

Original languageEnglish
Pages (from-to)59-65
Number of pages7
JournalPacific Journal of Mathematics
Volume52
Issue number1
DOIs
Publication statusPublished - May 1974

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ASJC Scopus subject areas

  • Mathematics(all)

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