On the monotonicity of the sequence (σ_k / σ*_k)

József Sándor
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 15, 2009, Number 3, Pages 9–13
Full paper (PDF, 157 Kb)

Details

Authors and affiliations

József Sándor
Babeș-Bolyai University of Cluj, Romania

Abstract

We prove that the sequence of ratios of the k-th powers of divisors, resp. unitary divisors of a number, is decreasing upon k.

Keywords

• Arithmetic functions
• Inequalities

AMS Classification

• 11A25

References

1. K. T. Atanassov, Remark on József Sándor and Florian Luca’s theorem, C. R. Acad. Bulg. Sci. 55(2002), no. 10, 9-14.
2. P. Erdős, Amer. Math. Monthly 58(1951), p. 98.
3. M. Le, A conjecture concerning the Smarandache dual function, Smarandache Notion J. 14(2004), 153-155.
4. F. Luca, On a divisibility property involving factorials, C. R. Acad. Bulg. Sci. 53(2000), no. 6, 35-38.
5. P. Moree and H. Roskam, On an arithmetical function related to Euler’s totient and the discriminantor, Fib. Quart. 33(1995), 332- 340.
6. J. Sándor, On certain generalizations of the Smarandache function, Smarandache Notions J. 11(2000), no. 1-3, 202-212.
7. J. Sándor, On certain generalizations of the Smarandache function, Notes Number Theory Discr. Math. 5(1999), no. 2, 41-51.
8. A. Schinzel, Sur l’équation φ(x) = m, Elem. Math. 11(1956), 75-78.
9. F. Smarandache, A function in the number theory, An. Univ. Timișoara, Ser. Mat., 38(1980), 79-88.
10. J. Sándor, On values of arithmetical functions at factorials, I, Smarandache Notions J., 10(1999), 87-94.