On a sum involving the number of distinct prime factors function related to the integer part function

Mihoub Bouderbala and Meselem Karras
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367-8275
Volume 26, 2020, Number 4, Pages 52–56
DOI: 10.7546/nntdm.2020.26.4.52-56
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Authors and affiliations

Mihoub Bouderbala
Institute of Mathematics-USTHB, LA3C
Houari-Boumédiène University of Science and Technology
Bab Ezzouar, Algeria

Meselem Karras
Djilali Bounaama Khemis Miliana University
FIMA Laboratory, Algeria

Abstract

In this paper, we obtain asymptotic formula on the sum \sum\limits_{n\leq x}\omega \left( \left\lfloor \frac{x}{n}\right\rfloor \right) , where \omega \left( n\right) denote the number of distinct prime divisors of n and \left\lfloor t\right\rfloor denotes the integer part of t.

Keywords

  • Number of distinct prime divisors
  • Mean value
  • Integer part

2010 Mathematics Subject Classification

  • 11N37
  • 11A25
  • 11N36.

References

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  3. Diaconis, (1976). Asymptotic expansions for the mean and variance of the number of prime factors of a number n, Technical Report No. 96, Department of Statistics, Stanford University.
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Cite this paper

Bouderbala, M. & Karras, M. (2020). On a sum involving the number of distinct prime factors function related to the integer part function. Notes on Number Theory and Discrete Mathematics, 26 (4), 52-56, DOI: 10.7546/nntdm.2020.26.4.52-56.

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