Two Remarks on the Largest Prime Factors of n and n + 1
Sungjin Kim
Department of Mathematics
Santa Monica College
California State University, Northridge
18111 Nordhoff Street
Northridge, CA 91330
USA
Abstract:
Let P(n) be the largest prime factor of n. We give
an alternative proof of the existence of infinitely many n such
that P(n) > P(n + 1) > P(n
+ 2). Further, we prove that the
set {P(n+1)/P(n)}n∈N
has infinitely many limit points
{0, xn, 1, yn}n∈N
with 0 < xn < 1 < yn and
lim xn = lim yn = 1.
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(Concerned with sequence
A006530.)
Received June 15 2020;
revised versions received September 7 2020; October 16 2020.
Published in Journal of Integer Sequences,
October 16 2020.
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