(1.2) log2 pj ≤ αj + β (1 ≤ j ≤ ω(n)), where α ≥ 0 and log2 y denotes log log y. The distribution of integers satisfying (1.1) is important in the study of the distribution of divisors of integers (see [3]; Ch. 2 of [4]). We present here estimates for Nk(x;α, β) = #{n ≤ x : ω(n) = k, (1.1)}, Mk(x;α, β) = #{n ≤ x : ω(n) = k, (1.2)}. It is a relatively simple matter, at least heuristically, to re...
