Sunanta Srisopha, Teerapat Srichan and Sukrawan Mavecha
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 3, Pages 435–440
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Let P be a finite set of prime numbers. By using an elementary method, the proportion of all r-free numbers which are divisible by at least one element in P is studied.
- Natural density
- r-free number
2020 Mathematics Subject Classification
- Brown, R. (2021). The natural density of some sets of square-free numbers. Integers, A81.1-9.
- Hardy, G. H., & Wright, E. M. (1979). An Introduction to the Theory of Numbers (5th ed.). Oxford University Press, Oxford.
- Jameson, G. J. O. (2010). Even and odd square-free numbers. The Mathematical Gazette, 94, 123–127.
- Jameson, G. J. O. (2021). Revisiting even and odd square-free numbers. The Mathematical Gazette, 105, 299–300.
- Puttasontiphot, T., & Srichan, T. (2021). Odd/even cube-full numbers. Notes on Number Theory and Discrete Mathematics, 27(1), 27–31.
- Scott, J. A. (2008). Square-free integers once again. The Mathematical Gazette, 92, 70–71.
- Srichan, T. (2020). The odd/even dichotomy for the set of square-full numbers. Applied Mathematics E-Notes, 20, 528–531.
- Srisopha, S., Srichan, T., & Mavecha, S. Odd/even r-free numbers. Applied Mathematics E-Notes (to appear).
- Received: 9 March 2022
- Revised: 24 June 2022
- Accepted: 7 July 2022
- Online First: 20 July 2022
Cite this paper
Srisopha, S., Srichan, T., & Mavecha, S. (2022). Note on the natural density of r-free numbers. Notes on Number Theory and Discrete Mathematics, 28(3), 435-440, DOI: 10.7546/nntdm.2022.28.3.435-440.