# 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 language English 59-65 7 Pacific Journal of Mathematics 52 1 Published - 1974

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Multiplicative
Distribution Function
Integer
Estimate
Form

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

In: Pacific Journal of Mathematics, Vol. 52, No. 1, 1974, p. 59-65.

Research output: Contribution to journalArticle

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