A remark on the number of distinct prime divisors of integers

Authors

  • Mehdi Hassani University of Zanjan

DOI:

https://doi.org/10.5556/j.tkjm.48.2017.1842

Keywords:

Prime number, arithmetic function

Abstract

We study the asymptotic formula for the sum $\sum_{n\leqslant x}\o(n)$ where $\o(n)$ denotes the number of distinct prime divisors of $n$, and we perform some computations which detect curve patterns in the distribution of a related sequence.

Author Biography

Mehdi Hassani, University of Zanjan

Department ofMathematics, University of Zanjan, University Blvd., 45371-38791, Zanjan, Iran.

References

S. R. Finch, Mathematical constants, Encyclopedia of Mathematics and its Applications, 94, Cambridge University Press, Cambridge, 2003.

G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number $n$, Quart. J. Math., 48(1917), 76--92.

J. Lee, The second central moment of additive functions, Proc. Amer. Math. Soc., 114(1992), 887--895.

J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math., 6 (1962), 64--94.

C. de la Vallee Poussin, Sur les valeurs moyennes de certaines fonctions arithmetiques, Annales de la

societe scientifique de Bruxelles, 22(1898), 84--90.

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Published

2017-03-30

How to Cite

Hassani, M. (2017). A remark on the number of distinct prime divisors of integers. Tamkang Journal of Mathematics, 48(1), 13–15. https://doi.org/10.5556/j.tkjm.48.2017.1842

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Section

Papers