A remark on the number of distinct prime divisors of integers

Mehdi Hassani

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.

Keywords


Prime number, arithmetic function

Full Text:

PDF

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.




DOI: http://dx.doi.org/10.5556/j.tkjm.48.2017.1842

Sponsored by Tamkang University | ISSN 0049-2930 (Print), ISSN 2073-9826 (Online) | Powered by MathJax