... ω(n) is the number of distinct prime 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 ... of Mathematics, 168 (2008), 367–433 The distribution of integers with a divisorin a given intervalBy Kevin FordAbstractWe determine the order of magnitude of H(x, y, z), the number of in-tegers ... for r ≥ 2 and z ≥ yC(see the conjec-ture at the end of §5).(iii) Establish the order of Hr(x, y, z) when yz ≥ x1−c.(iv) Make the dependence on r explicit in Theorem 5 and Corollary 7....