Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] H. Halberstam, On integers all of whose prime factors are small, Proc. London Math. Soc. (3) 21 (1970), 102-107. MR 42 #4509. MR 0269614 (42:4509)
  • [2] 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 48 #8363. MR 0330024 (48:8363)
  • [3] D. G. Hazlewood, On integers all of whose prime factors are small, Bull. London Math. Soc. 5 (1973), 159-163. MR 0337846 (49:2615)
  • [4] -, Sums over positive integers with few prime factors, J. Number Theory 7 (1975), 189-207. MR 0371835 (51:8052)
  • [5] B. V. Levin and A. S. Fainleib, Application of certain integral equations to questions of the theory of numbers, Uspehi Mat. Nauk 22 (1967), no. 3 (135), 119-197 = Russian Math. Surveys 22 (1967), no. 3, 119-204. MR 37 #5174. MR 0229600 (37:5174)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10H25

Retrieve articles in all journals with MSC: 10H25


Additional Information

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

American Mathematical Society