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The Error Term for the Squarefree Integers

Published online by Cambridge University Press:  20 November 2018

L. Moser  and
R.A. MacLeod
L. Moser
Affiliation:
University of Alberta, Edmonton
R.A. MacLeod
Affiliation:
University of Alberta, Edmonton
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Let Q(x) denote the number of squarefree integers ≤ x. Recently K. Rogers [ l ] has shown that Q(x) ≥ 53x / 88 for all x, with equality only at x = 176. Define R(x) to be Q(x) - 6/п2 X. (We observe that and ) Our objective will be to examine R(x). In particular, we show that for all x and observe that for x ≥ 8.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 3 , August 1966 , pp. 303 - 306
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Rogers, K., The Schnirelmann density of the squarefree integers, Proc. Amer. Math. Soc. 15(1964), 515-516.Google Scholar
2. Landau, E., Vorlesungen Uber Zahlentheorie, II, Chelsea (1947).Google Scholar
3. Evelyn, C. J. A. and Linfoot, E.H., On a problem in the additive theory of numbers (Fourth paper). Ann. of Math. 32(1931) 261-270.Google Scholar