On certain inequalities for σ, φ, ψ and related functions

József Sándor
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 2, Pages 52—60
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Authors and affiliations

József Sándor
Babeș-Bolyai University, Department of Mathematics
Str. Kogălniceanu nr. 1, 400084 Cluj-Napoca, Romania

Abstract

Some new inequalities for the arithmetic functions of the title are considered. Among others we offer a refinement of a recent arithmetic inequality by K. T. Atanassov [1].

Keywords

  • Arithmetic functions
  • Inequalities for arithmetic functions
  • Inequalities of Weierstrass type

AMS Classification

  • 11A25
  • 26D99

References

  1. Atanassov, K. T. Note on φ, ψ and σ-functions. Part 6. Notes Numb. Th. Discr. Math., Vol. 19, 2013, No. 1, 22–24.
  2. Sándor, J., L. Tóth. On certain number-theoretic inequalities. Fib. Quart., Vol. 28, 1990, 255–258.
  3. Sándor, J., D. S. Mitrinović, B. Crstici, Handbook of number theory I, Springer Verlag, 2006 (first edition by Kluwer, 1995).
  4. Sándor, J. On certain inequalities for arithmetic functions. Notes Numb. Theor. Discr. Math., Vol. 1, 1995, No. 1, 27–32.
  5. Sándor, J. On inequalities \sigma(n) > n + \sqrt(n) and \sigma(n) > n + \sqrt(n) + \sqrt[3](n). Octogon Math. Mag., Vol. 16, 2008, No. 1, 276–278.
  6. Sándor, J. On the inequality \sigma(n) < \fract{\pi^2}{6} . \psi(n). Octogon Math. Mag., Vol. 16, 2008, No. 1, 295–296.

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Cite this paper

APA

Sándor, J. (2014). On certain inequalities for σ, φ, ψ and related functions. Notes on Number Theory and Discrete Mathematics, 20(2), 52-60.

Chicago

Sándor, József. “On certain inequalities for σ, φ, ψ and related functions.” Notes on Number Theory and Discrete Mathematics 20, no. 2 (2014): 52-60

MLA

Sándor, József. “On certain inequalities for σ, φ, ψ and related functions.” Notes on Number Theory and Discrete Mathematics 20.2 (2014): 52-60. Print.

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