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

abstract

  • For a > 0 let a(x, y) = a(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 a(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.

published proceedings

  • Journal of Number Theory

author list (cited authors)

  • Hensley, D.

citation count

  • 3

complete list of authors

  • Hensley, Douglas

publication date

  • January 1984