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$%W. D. Banks, F. Luca, and I. E. Shparlinski, On rough and smooth neighbors, Rev. Mat. Complut. 20 (2007), no. 1, 109–118. %$

On Rough and Smooth Neighbors
William D. BANKS, Florian LUCA,
and Igor E. SHPARLINSKI
Department of Mathematics
University of Missouri
Columbia, MO 65211 — USA

bbanks@math.missouri.edu
Instituto de Matemáticas
Universidad Nacional Autónoma de México
C.P. 58089, Morelia, Michoacán, México

fluca@matmor.unam.mx
Department of Computing
Macquarie University
Sydney, NSW 2109 — Australia

igor@ics.mq.edu.au

Received: November 2, 2005
Accepted: June 19, 2006

ABSTRACT

We study the behavior of the arithmetic functions defined by

        P +(n)              P +(n+ 1)
F (n) = P-(n+-1)- and  G(n)= --P-(n)--   (n≥ 1),

where P+(k) and P-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k .

Key words: smallest prime divisor, largest prime divisor.
2000 Mathematics Subject Classification:
11N25, 11N64.