**Krassimir T. Atanassov**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 28, 2022, Number 3, Pages 558–563

DOI: 10.7546/nntdm.2022.28.3.558-563

**Full paper (PDF, 158 Kb)**

## Details

### Authors and affiliations

Krassimir T. Atanassov

^{1} Department of Bioinformatics and Mathematical Modelling,

Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences,

Acad. G. Bonchev Str. Bl. 105, Sofia-1113, Bulgaria

^{2} Intelligent Systems Laboratory, “Prof. Dr. Asen Zlatarov” University

Bourgas-8010, Bulgaria

### Abstract

The set *Set*(*n*), generated by an arbitrary natural number *n*, was defined in [2] and some arithmetic functions, defined over its elements are introduced in an algebraic aspect. Here, over the elements of *Set*(*n*), two arithmetic functions similar to the modal type of operators are defined and some of their basic properties are studied.

### Keywords

- Arithmetic functions
- Modal operators
- Natural numbers
- Sets

### 2020 Mathematics Subject Classification

- 11A25

### References

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### Manuscript history

- Received: 20 January 2022
- Revised: 17 July 2022
- Accepted: 7 September 2022
- Online First: 19 September 2022

## Related papers

- Atanassov, K. (2020). Objects generated by an arbitrary natural number.
*Notes on Number Theory and Discrete Mathematics*, 26 (4), 57-62. - Atanassov, K. (2023). Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect.
*Notes on Number Theory and Discrete Mathematics*, 29(1), 171-180. - Atanassov, K. (2023). Objects generated by an arbitrary natural number. Part 4: New aspects.
*Notes on Number Theory and Discrete Mathematics*, 29(3), 589-597.

## Cite this paper

Atanassov, K. T. (2022). Objects generated by an arbitrary natural number. Part 2: Modal aspect. *Notes on Number Theory and Discrete Mathematics*, 28(3), 558-563, DOI: 10.7546/nntdm.2022.28.3.558-563.