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On the Sum of the Reciprocals of the Middle Prime Factors of an Integer
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Vincent Ouellet

Département de mathématiques et de statistique

Université Laval

Québec G1V 0A6

Canada

**Abstract:**

We consider the arithmetical function
*p*^{(β)}(*n*) :=
*p*_{max(1,⌊ βk⌋)}
for a given fixed number β ∈ (0,1),
where *p*_{1} <
*p*_{2} < ยทยทยท < *p*_{k}
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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