Let (un)n≥0 be a non-degenerate linear recurrence sequence of integers. We show that the set of positive integers n such that either ω(n) or Ω(n) divides un is of asymptotic density zero, where ω(n) and Ω(n) are the numbers of prime and prime power divisors of n, respectively. The same also holds for the set of positive integers n such that τ(n) un, where τ(n) is the number of the positive integer divisors of n, provided that un satisfies some mild technical conditions.
|Number of pages||14|
|Journal||Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg|
|Publication status||Published - 2006|