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Distinct values of Euler's ø-function

Published online by Cambridge University Press:  26 February 2010

P. Erdős  and
R. R. Hall
P. Erdős
Affiliation:
Department of Mathematics, University of York, England
R. R. Hall
Affiliation:
Department of Mathematics, University of York, England
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Extract

Let V(x) denote the number of distinct values not exceeding x taken by Euler's ø-function, so that we have π(x) ≤ V(x) ≤ x. It was shown by Erdős and Hall [1] that for each fixed B > 2√(2/log 2), the estimate

holds; moreover we stated that the ratio V(x)/π(x) tends to infinity with x, faster than any fixed power of log log x. Our aim in the present paper is to prove the following result.

Type
Research Article
Information
Mathematika , Volume 23 , Issue 1 , June 1976 , pp. 1 - 3
Copyright
Copyright © University College London 1976

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References

1.Erdős, P. and Hall, R. R.. “On the values of Euler's ø-function”, Ada Arithmetica, 22 (1973), 201–206.Google Scholar
2.Prachar, K.. Primzahlverteiltung (Springer, 1957).Google Scholar