### 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 |
---|---|

Pages (from-to) | 59-65 |

Number of pages | 7 |

Journal | Pacific Journal of Mathematics |

Volume | 52 |

Issue number | 1 |

Publication status | Published - 1974 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On the distribution of numbers of the form σ(N)/n and on some related questions.** / Erdős, P.

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 52, no. 1, pp. 59-65.

}

TY - JOUR

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

AU - Erdős, P.

PY - 1974

Y1 - 1974

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.

UR - http://www.scopus.com/inward/record.url?scp=33745678591&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745678591&partnerID=8YFLogxK

M3 - Article

VL - 52

SP - 59

EP - 65

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -