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On the Distance Between Consecutive Divisors of an Integer

Published online by Cambridge University Press:  20 November 2018

Jean-Marie de Koninck  and
Aleksandar Ivić
Jean-Marie de Koninck
Affiliation:
Département De Mathématiques, Université LavalG1K 7P4, Québec, Canada
Aleksandar Ivić
Affiliation:
Katedra MatematikeRgf-A Universiteta U Beogradu Djusina 7, 11000, Beograd Jugoslavija
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Abstract

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Let ω(n) denote the number of distinct prime divisors of a positive integer n. Then we define and where are primes and r ≥ 2. Similarly denote by the number of divisors of n and let be defined by where are the divisors of n. We prove that there exists constants A and B such that and

Keywords

Primary 10H25Secondary 10H32
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 2 , 01 June 1986 , pp. 208 - 217
Copyright
Copyright © Canadian Mathematical Society 1986

References

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