Prime counting function in base of x/3

Abstract

In this study, we present the function H(x)p based on Pk(x, a) introduced by Lehmer. H(x)p denotes the number of numbers that are not divisible by prime numbers < p but are divisible by p. Herein, we show that H(x)p can be obtained only using x 3 . We also present our own prime counting function based on H(x)p, that is, x 3 . Mathematics Subject Classification: 11A41, 11N05