Journal of Integer Sequences, Vol. 20 (2017), Article 17.10.1

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


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 nx, 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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