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Beurling numbers whose number of prime factors lies in a specified residue class

Volume 196 / 2020

Gregory Debruyne Acta Arithmetica 196 (2020), 433-438 MSC: 11N25, 11N37, 11N80. DOI: 10.4064/aa200130-15-6 Published online: 31 August 2020


We find the asymptotics for $S_{K,c}(x)$, the number of positive integers below $x$ whose number of prime factors is $c \bmod K$. We study this question in the context of Beurling integers.


  • Gregory DebruyneDepartment of Mathematics: Analysis, Logic and Discrete Mathematics
    Ghent University
    Krijgslaan 281, Gebouw S8
    B-9000 Gent, Belgium

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