International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 5, Pages 307-311
doi:10.1155/S0161171201005725
Properties of the function f(x)=x/π(x)
Hellenic Open University, Greece
Received 21 August 2000
Copyright © 2001 Panayiotis Vlamos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We obtain the asymptotic estimations for ∑k=2nf(k) and ∑k=2n1/f(k), where f(k)=k/π(k), k≥2. We study the expression 2f(x+y)−f(x)−f(y) for integers x,y≥2 and
as an application we make several remarks in connection with the
conjecture of Hardy and Littlewood.