THE UNIFORM DISTRIBUTION mod~1 OF SEQUENCES INVOLVING THE LARGEST PRIME FACTOR FUNCTION

Author:

Jean-Marie~DE~KONINCK,~Imre~K\'ATAI

2010 Mathematics Subject Classification:

11K16, 11N37, 11N41.

Keywords:

largest prime factor, normal numbers.

Abstract:

Let P(n) stand for the largest prime factor of n, and let f be a real valued function satisfying certain conditions. We prove that  the sequence (f(P(n)))_{n\geq 2} is uniformly distributed modulo 1. We also show an analogous result if P(n) is replaced by P_k(n), the kth largest prime factor of n.

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Koni-Kata-2013

Vol. 8 (16), 2013