Type: Article

On strings of consecutive integers with a distinct number of prime factors

Jean-Marie De Koninck; John B. Friedlander; Florian Luca;

Abstract:

Let omega(n) be the number of distinct prime factors of n. For any positive integer k let n = n(k) be the smallest positive integer such that omega(n + 1),...,omega(n + k) are mutually distinct. In this paper, we give upper and lower bounds for n(k). We study the same quantity when omega(n) is replaced by Omega(n), the total number of prime factors of n counted with repetitions.