On integers free of large prime factors
Authors:
Adolf Hildebrand and Gérald Tenenbaum
Journal:
Trans. Amer. Math. Soc. 296 (1986), 265-290
MSC:
Primary 11N25
DOI:
https://doi.org/10.1090/S0002-9947-1986-0837811-1
MathSciNet review:
837811
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Abstract | References | Similar Articles | Additional Information
Abstract: The number of integers
and free of prime factors
has been given satisfactory estimates in the regions
and
. In the intermediate range, only very crude estimates have been obtained so far. We close this "gap" and give an expression which approximates
uniformly for
within a factor
. As an application, we derive a simple formula for
, where
. We also prove a short interval estimate for
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1986-0837811-1
Article copyright:
© Copyright 1986
American Mathematical Society