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Carmichael Numbers with a Square Totient

Published online by Cambridge University Press:  20 November 2018

W. D. Banks
W. D. Banks*
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211 USA e-mail: bbanks@math.missouri.edu
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Abstract

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Let $\varphi$ denote the Euler function. In this paper, we show that for all large $x$ there are more than ${{x}^{0.33}}$ Carmichael numbers $n\,\le \,x$ with the property that $\varphi \left( n \right)$ is a perfect square. We also obtain similar results for higher powers.

Keywords

11N2511A25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 3 - 8
Copyright
Copyright © Canadian Mathematical Society 2009

References

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