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International Journal of Mathematics and Mathematical Sciences
Volume 28, Issue 5, Pages 307-311
http://dx.doi.org/10.1155/S0161171201005725

Properties of the function f(x)=x/π(x)

Hellenic Open University, Greece

Received 21 August 2000

Copyright © 2001 Hindawi Publishing Corporation. 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), k2. We study the expression 2f(x+y)f(x)f(y) for integers x,y2 and as an application we make several remarks in connection with the conjecture of Hardy and Littlewood.