The sum of aΩ(n) over integers n ≤ x with all prime factors between a and y Academic Article uri icon


  • For a > 0 let ψa(x, y) = ΣaΩ(n), the sum taken over all n, 1 ≤ n ≤ x such that if p is prime and p|n then a < p ≤ y. It is shown for u < about ( log log x log log log x) that ψa(x, x 1 u) {reversed tilde equals} x(log x)a-1pa(u), where pa(u) solves a delay differential equation much like that for the Dickman function p(u), and the asymptotic behavior of pa(u) is worked out. © 1984.

author list (cited authors)

  • Hensley, D.

citation count

  • 3

publication date

  • April 1984