TY - JOUR

T1 - On the distribution of numbers of the form σ(N)/n and on some related questions

AU - Erdös, P.

PY - 1974/5

Y1 - 1974/5

N2 - 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.

AB - 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.

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U2 - 10.2140/pjm.1974.52.59

DO - 10.2140/pjm.1974.52.59

M3 - Article

AN - SCOPUS:33745678591

VL - 52

SP - 59

EP - 65

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -