Solutions of d(n)=d(Ï•(n)) where n has four different prime divisors
Solutions of d(n)=d(Ï•(n)) where n has four different prime divisors
DOI :
https://doi.org/10.5269/bspm.66243Résumé
For a positive integer n, let d(n), ϕ(n) and ω(n) denote the number of positive divisors of n, the Euler's phi function of n and the number of different prime divisors of n, respectively. In this paper, we focus on positive integers n such that d(n)=d(ϕ(n)) and ω(n)=4.
Références
1. Z. Amroune, D. Bellaouar and A. Boudaoud, A class of solutions of the equation d(n2) = d ( (n)), Notes on Number Theory and Discrete Mathematics, 29(2) (2023), 284–309.
2. Z. Amroune, D. Bellaouar and A. Boudaoud, Solutions of the equation d (kn) = ( (n)). Jordan Journal of Mathematics and Statistics 17 (2024), No. 3, 317-324.
3. D. Bellaouar, A. Boudaoud and O. Ozer, On a sequence formed by iterating a divisor operator, Czech. Math. J., 69 (144) (2019), 1177–1196.
4. D. Bellaouar, A. Boudaoud and R. Jakimczuk, Notes on the equation d(n) = d((n)) and related inequalities. Math. Slovaca, V. 73. Nâ—¦ 4 (2023), 613–632.
5. D. Bellaouar, A. Togbe and R. Jakimczuk, New notes on the equation d(n) = d((n)) and the inequality d (n) > d ( (n)), Math. Slovaca, V 74, No. 5 (2024), 1127-1146.
6. J. M. De Koninck and A. Mercier, 1001 problems in classical number theory, Providence, RI: American Mathematical Society (2007).
7. H. Dubner, Large Sophie Germain primes, Mathematics of computation, 65(213) (1996), 393–396.
8. R. K. Guy, Unsolved problems in number theory, Springer-Verlag, New York, 2 edition (1994).
9. D. E, Iannucci, On the equation σ(n) = n + (n), J. Integer Seq., 20 (2017), Article 17.6.2.
10. F. Liu, On the Sophie Germain prime conjecture, WSEAS Transactions on mathematics, 10(12) (2011), 421–430.
11. F. Luca, Equations involving arithmetic functions of factorials, Divulg. Mat., 8 (2000), 15–23.
12. M. B. Nathanson, Elementary methods in number theory, Springer-Verlag, New York, (2000).
13. J. Sandor, Geometric theorems, Diophantine equations, and arithmetic functions. American Research Press. Rehoboth, 2002.
2. Z. Amroune, D. Bellaouar and A. Boudaoud, Solutions of the equation d (kn) = ( (n)). Jordan Journal of Mathematics and Statistics 17 (2024), No. 3, 317-324.
3. D. Bellaouar, A. Boudaoud and O. Ozer, On a sequence formed by iterating a divisor operator, Czech. Math. J., 69 (144) (2019), 1177–1196.
4. D. Bellaouar, A. Boudaoud and R. Jakimczuk, Notes on the equation d(n) = d((n)) and related inequalities. Math. Slovaca, V. 73. Nâ—¦ 4 (2023), 613–632.
5. D. Bellaouar, A. Togbe and R. Jakimczuk, New notes on the equation d(n) = d((n)) and the inequality d (n) > d ( (n)), Math. Slovaca, V 74, No. 5 (2024), 1127-1146.
6. J. M. De Koninck and A. Mercier, 1001 problems in classical number theory, Providence, RI: American Mathematical Society (2007).
7. H. Dubner, Large Sophie Germain primes, Mathematics of computation, 65(213) (1996), 393–396.
8. R. K. Guy, Unsolved problems in number theory, Springer-Verlag, New York, 2 edition (1994).
9. D. E, Iannucci, On the equation σ(n) = n + (n), J. Integer Seq., 20 (2017), Article 17.6.2.
10. F. Liu, On the Sophie Germain prime conjecture, WSEAS Transactions on mathematics, 10(12) (2011), 421–430.
11. F. Luca, Equations involving arithmetic functions of factorials, Divulg. Mat., 8 (2000), 15–23.
12. M. B. Nathanson, Elementary methods in number theory, Springer-Verlag, New York, (2000).
13. J. Sandor, Geometric theorems, Diophantine equations, and arithmetic functions. American Research Press. Rehoboth, 2002.
Téléchargements
Publié
2025-02-12
Numéro
Rubrique
Research Articles
Licence
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
Comment citer
Bellaouar, D., & Bouhadjar, S. (2025). Solutions of d(n)=d(Ï•(n)) where n has four different prime divisors: Solutions of d(n)=d(Ï•(n)) where n has four different prime divisors. Boletim Da Sociedade Paranaense De Matemática, 43, 1-19. https://doi.org/10.5269/bspm.66243
