On new arithmetic function relative to a fixed positive integer. Part 1

Brahim Mittou and Abdallah Derbal
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 22—26
DOI: 10.7546/nntdm.2021.27.1.22-26
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Authors and affiliations

Brahim Mittou
Department of Mathematics, University Kasdi Merbah, Ouargla
EDPNL & HM Laboratory, ENS of Kouba, Algiers, Algeria

Abdallah Derbal
ENS of Kouba, Algiers
EDPNL & HM Laboratory, ENS of Kouba, Algiers, Algeria

Abstract

The main purpose of this note is to define a new arithmetic function relative to a fixed positive integer and to study some of its properties.

Keywords

  • Arithmetic function
  • Greatest common divisor

2010 Mathematics Subject Classification

  • 11A25

References

  1. Atanassov, K. (1987). New integer functions, related to φ and σ functions. Bulletin of Number Theory and Related Topics, XI(1), 3–26.
  2. Atanassov, K. (2002). Restrictive factor: Definition, properties and problems. Notes on Number Theory and Discrete Mathematics, 8(4), 117–119.
  3. Atanassov, K. (2016). An arithmetic function decreasing the natural numbers. Notes on Number Theory and Discrete Mathematics, 22(4), 16–19.
  4. Atanassov, K. (2016). On function ”Restrictive factor”. Notes on Number Theory and Discrete Mathematics, 22(2), 17–22.
  5. Atanassov, K. & Sandor, J. (2019). Extension factor: Definition, properties and problems. Part 1. Notes on Number Theory and Discrete Mathematics, 25(3), 36–43.
  6. Atanassov, K. & Sandor, J. (2020). Extension factor: Definition, properties and problems. Part 2. Notes on Number Theory and Discrete Mathematics, 26(1), 31–39.
  7. Defant, C. (2018). Connected components of complex divisor functions. Journal of Number Theory, 190, 56–71.
  8. Hoque, A., & Kalita, H. (2014). Generalized Perfect Numbers Connected with Arithmetic Functions. Mathematical Sciences Letters, 3(3), 249–253.
  9. Hoque, A., & Saikia, H. K. (2014). On generalized Mersenne prime. SeMA Journal, 66(1), 1–7.
  10. Hoque, A., & Saikia, H. K. (2015). On generalized Mersenne primes and class-numbers of equivalent quadratic fields and cyclotomic fields. SeMA Journal, 67(1), 71–75.
  11. McCarthy, P. J. (1959). On an arithmetic function. Monatshefte fur Mathematik, 63, 228–230

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Cite this paper

Mittou, B. & Derbal, A. (2021). On new arithmetic function relative to a fixed positive integer. Part 1. Notes on Number Theory and Discrete Mathematics, 27(1), 22-26, doi: 10.7546/nntdm.2021.27.1.22-26.

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