On the Sum of the Reciprocals of the Middle Prime Factors of an Integer
Vincent Ouellet
Département de mathématiques et de statistique
Université Laval
Québec G1V 0A6
Canada
Abstract:
We consider the arithmetical function
p(β)(n) :=
pmax(1,⌊ βk⌋)
for a given fixed number β ∈ (0,1),
where p1 <
p2 < ยทยทยท < pk
are the prime factors of n.
We provide an estimate for the sum of the
reciprocals of p(β)(n)
for n ≤ x,
which improves and generalizes an earlier result of De Koninck and Luca.
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Received September 14 2017; revised version received October 1 2017.
Published in Journal of Integer Sequences, October 29 2017.
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