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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
DOI: https://doi.org/10.1090/S0002-9939-1975-0374056-4
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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Keywords: Numbers with small prime factors, <IMG WIDTH="17" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$k$">-free integers, Buchstab identity
Article copyright: © Copyright 1975 American Mathematical Society