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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

1. De Koninck, J.-M. and Ivic, A., The distribution of the average prime divisor of an integer, Arch. Math., 43 (1984), pp. 37–43.Google Scholar
2. De Koninck, J.-M. and Ivic, A., Topics in arithmetical functions, Mathematics Studies, 43, Amsterdam, 1980.Google Scholar
3. Erdös, P. and A. Rényi, Some problems and results on consecutive primes, Simon Stevin, 27 (1950), pp. 115–125.Google Scholar
4. Maier, H. and Tenenbaum, G., On the set of divisors of an integer, Invent. Math., 76 (1984), pp. 121–128.Google Scholar
5. Montgomery, H.L., Topics in multiplicative number theory, LNM 227, (Berlin-Heidelberg-New York, 1971).Google Scholar