## On $k$-free integers with small prime factors

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- by D. G. Hazlewood PDF
- Proc. Amer. Math. Soc.
**52**(1975), 40-44 Request permission

## 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 $y$.## References

- H. Halberstam,
*On integers all of whose prime factors are small*, Proc. London Math. Soc. (3)**21**(1970), 102–107. MR**269614**, DOI 10.1112/plms/s3-21.1.102 - V. C. Harris and M. V. Subbarao,
*An arithmetic sum with an application to quasi $k$-free integers*, J. Austral. Math. Soc.**15**(1973), 272–278. MR**0330024**, DOI 10.1017/S1446788700013185 - D. G. Hazlewood,
*On integers all of whose prime factors are small*, Bull. London Math. Soc.**5**(1973), 159–163. MR**337846**, DOI 10.1112/blms/5.2.159 - D. G. Hazlewood,
*Sums over positive integers with few prime factors*, J. Number Theory**7**(1975), 189–207. MR**371835**, DOI 10.1016/0022-314X(75)90016-5 - B. V. Levin and A. S. Faĭnleĭb,
*Application of certain integral equations to questions of the theory of numbers*, Uspehi Mat. Nauk**22**(1967), no. 3 (135), 119–197 (Russian). MR**0229600**

## Additional Information

- © Copyright 1975 American Mathematical Society
- 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