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