**Sunanta Srisopha and Teerapat Srichan**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 2, Pages 427–435

DOI: 10.7546/nntdm.2024.30.2.427-435

**Full paper (PDF, 246 Kb)**

## Details

### Authors and affiliations

Sunanta Srisopha

*Department of Mathematics, Faculty of Science,
Valaya Alongkorn Rajabhat University under the Royal Patronage Pathum Thani Province,
Pathumthani 13180, Thailand*

Teerapat Srichan

*Department of Mathematics, Faculty of Science,
Kasetsart University
Bangkok 10900, Thailand*

### Abstract

Let . For , a lattice point is powerful if and only if is a powerful number, where is the greatest common divisor function. In this paper, we count the number of the ordered pairs , such that the lattice point is powerful. Moreover, we study -free lattice points analogues of powerful lattice points.

### Keywords

- Greatest common divisor
- Piatetski-Shapiro sequence
- -free lattice points

### 2020 Mathematics Subject Classification

- 11N37
- 11N45

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### Manuscript history

- Received: 11 April 2023
- Revised: 6 June 2024
- Accepted: 14 June 2024
- Online First: 20 June 2024

### Copyright information

Ⓒ 2024 by the Authors.

This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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## Cite this paper

Srisopha, S., & Srichan, T. (2024). On the distribution of powerful and *r*-free lattice points. *Notes on Number Theory and Discrete Mathematics*, 30(2), 427-435, DOI: 10.7546/nntdm.2024.30.2.427-435.