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In a series of papers the author studied constructed formulae of n-th prime number pn, based on some arithmetic functions φ and σ (see, e.g. [3, 4]). Here a new arithmetic function will be introduced and used to construct a formula for pn. Probably, this formula will be simpler than the previous ones.
- Atanassov K., New integer functions, related to “φ” and “σ” functions, Bulletin of Number Theory and Related Topics, Vol. XI (1987), No. 1, 3-26.
- Atanassov K., Some assertions on “φ” and “σ” functions, Bulletin of Number Theory and Related Topics, Vol. XI (1987), No. 1, 50-63.
- Chandrasekharan K. Introduction to Analytic Number Theory. Springer-Verlag, Berlin, 1968.
- Nagell T., Introduction to number theory, John Wiley & Sons, New York, 1950.
- Atanassov, K. A new formula for the n-th prime number. Comptes Rendus de l’Academie Bulgare des Sciences, Vol. 54, 2001, No. 7, 5-6.
- Atanassov, K. On a new formula for the n-th prime number. Notes on Number Theory and Discrete Mathematics, Vol. 10, 2004, No. 1, 24.
- Mitrinović, D., M. Popadić, Inequalities in Number Theory. Nis, Univ. of Nis, 1978.
Cite this paper
Atanassov, K. (2009). A remark on an arithmetic function. Part 1. Notes on Number Theory and Discrete Mathematics, 15(1), 22-24.