On Exponentially Ternary 2-Free Integers

Abstract

Let n be any natural number. For n>1 , let its prime power factorization be n=Ï€p₁^α1. If the digit 2 does not appear in the ternary expansion (i.e. in the representation in the base 3) of α₁ for every i, then n is called an Exponentially Ternary 2-Free (ETF₂) number. By convention we regard 1 as an ETF₂ number. Let E be the class of all ETF₂ numbers. If we denote by E(x), the number of (positive) integers ≤x contained in E, then it is implicit in some results of Murty [3] that
E(x)=Ax+O(x^1/2).