| Issue |
RAIRO-Theor. Inf. Appl.
Volume 60, 2026
Diophantine Analysis and Related Topics (DART2025Z)
|
|
|---|---|---|
| Article Number | 22 | |
| Number of page(s) | 13 | |
| DOI | https://doi.org/10.1051/ita/2026022 | |
| Published online | 16 July 2026 | |
On the distribution of consecutive M-free integers
1
Department of Mathematics, Faculty of Science, Kasetsart University,
Bangkok
10900,
Thailand
2
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University,
Bangkok
10330,
Thailand
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
30
April
2026
Accepted:
21
June
2026
Abstract
Let M be a set of positive integers with its minimal element m ≥ 2. A positive integer n is called an M-free integer if every exponent of its prime factors is not contained in M. In this paper, we derive a weak asymptotic formula for the consecutive M-free integers by an elementary method. Some new results of this problem for special integers ((k, r)-integer, (k,r)-free integer, semi-r-free integer, unitarily r-free integer, exponentially odd integer, and almost exponentially even integer) are obtained.
Mathematics Subject Classification: 11A05 / 11A25 / 11N37
Key words: Asymptotic formula / consecutive square-free integer / M-free integer / square-free integer
© The authors. Published by EDP Sciences, 2026
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