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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On $ k$-free integers with small prime factors


Author: D. G. Hazlewood
Journal: Proc. Amer. Math. Soc. 52 (1975), 40-44
MSC: Primary 10H25
MathSciNet review: 0374056
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Abstract: The object of this note is to give a nontrivial lower estimate for the function $ {\psi _k}(x,y;h)$, defined to be the number of $ k$-free integers $ m$ such that $ 1 \leqslant m < x,\,(m,h) = 1$, and $ m$ has no prime factor greater than or equal to $ y$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0374056-4
Keywords: Numbers with small prime factors, $ k$-free integers, Buchstab identity
Article copyright: © Copyright 1975 American Mathematical Society