On the Sum of the Reciprocals of the Middle Prime Factors of an Integer
Département de mathématiques et de statistique
Québec G1V 0A6
We consider the arithmetical function
for a given fixed number β ∈ (0,1),
where p1 <
p2 < ··· < 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.
Full version: pdf,
Received September 14 2017; revised version received October 1 2017.
Published in Journal of Integer Sequences, October 29 2017.
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