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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.

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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