On the exponent average of integer sequences

Abstract

Let ω(m) denote the number of distinct prime factors of the integerm, let Ω(m) be the number of prime factors ofm counted with multiplicities. The exponent averageA(m) is defined byA(m)=Ω(m)/ω(m) form>1, andA(1)=1. If (mn) is a sequence of positive integers, we can study the asymptotic exponent average limn→∞A(mn) (if it exists) resp. lim sup and lim inf.