We consider the arithmetical function p(β)(n) := pmax(1,⌊ βk⌋) 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.
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