On two arithmetic functions

József Sándor and Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 48–53
Full paper (PDF, 162 Kb)

Details

Authors and affiliations

József Sándor
Babes-Bolyai University, Department of Mathematics,
Cluj-Napoca, Romania

Krassimir T. Atanassov
Dept. of Bioinformatics and Mathematical Modelling
Institute of Biophysics and Biomedical Engineering,
Bulgarian Academy of Sciences
105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria
and
Intelligent Systems Laboratory
Prof. Asen Zlatarov University, Bourgas-8010, Bulgaria

Abstract

Some properties of two new arithmetic functions are studied. Three conjectures are formulated.

Keywords

• Arithmetic function
• Natural number
• Prime number

AMS Classification

• 11A25

References

1. Atanassov, K. (2016) An arithmetic function decreasing the natural numbers. Notes on Number Theory and Discrete Mathematics, 22(4), 16–19.
2. Garsia, A. M. & Remmel, J. (1980) A combinatorial interpretation of q-derangement and q-Laguerre numbers, Europ. J. Combinatorics, 1, 47–59.
3. Maynard, J. (2015) Small gaps between primes, Annals of Mathematics, 181, 383–413.
4. Sándor, J., Mitrinovic, D. S., & Crstici, B. (2006) Handbook of number theory, Vol. I,
   Springer, Dordrecht.