... divisors of n, Ω(n) is the number of prime power divisors of n, π(x) is the number of primes ≤ x, τ(n) is the number of divisors of n. P(s, t) is the set of positive integers composed of prime ... author enjoyed the hospitality of the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. Finally, the author acknowledges the referee for a thorough reading of the paper and ... is the set of square-free members of P (s, t).We list a few estimates from prime number theory and sieve theory. The first is the Brun-Titchmarsh inequality and the second is a consequence of the Prime...