**André Pierro de Camargo**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 29, 2023, Number 3, Pages 549–556

DOI: 10.7546/nntdm.2023.29.3.549-556

**Full paper (PDF, 242 Kb)**

## Details

### Authors and affiliations

André Pierro de Camargo

*Federal University of the ABC Region, Brazil*

### Abstract

We obtain an asymptotic formula for the sum of the divisors of all square-free integers less than or equal to , with error term . This improves the error term presented in [7] obtained via analytical methods. Our approach is elementary and it is based on the connections between the function and unitary convolutions.

### Keywords

- Dirichlet divisor problem
- Square-free integers
- Unitary convolutions

### 2020 Mathematics Subject Classification

- 11N56
- 11N37

### References

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### Manuscript history

- Received: 11 April 2023
- Revised: 23 May 2023
- Accepted: 24 July 2023
- Online First: 27 July 2023

### Copyright information

Ⓒ 2023 by the Author.

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).

## Related papers

- Jakimczuk, R., & Lalín, M. (2022). Asymptotics of sums of divisor functions over sequences with restricted factorization structure.
*Notes on Number Theory and Discrete Mathematics*, 28(4), 617–634.

## Cite this paper

Camargo, A. P. (2023). The Dirichlet divisor problem over square-free integers and unitary convolutions. *Notes on Number Theory and Discrete Mathematics*, 29(3), 549-556, DOI: 10.7546/nntdm.2023.29.3.549-556.