JIPAM

A Note on Sándor Type Functions  
 
  Authors: N. Anitha,  
  Keywords: Asymptotic formula, Infinite Series.  
  Date Received: 14/06/05  
  Date Accepted: 28/07/05  
  Subject Codes:

40A05, 33E99.

  
  Editors: Jozsef Sandor,  
 
  Abstract:

In this paper we introduce the functions G and $ G_{ast}$ similar to Sándor's functions which are defined by,

$displaystyle G(x) = min{min mathbb{N}: xleq e^{m}}, quad x in [1,infty),$    

$displaystyle G_{ast}(x) = max{min mathbb{N}: e^{m}leq x}, quad x in [e,infty).bigskip$    

We study some interesting properties of G and $ G_{ast}$. The main purpose of this paper is to show that
$displaystyle pi(x) simfrac{x}{G_{ast}(x)} bigskip$    

where $ pi(x)$ is the number of primes less than or equal to $ x$.;


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