Carmichael Numbers with a Square Totient
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.
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| Veröffentlicht in: | Canadian mathematical bulletin 2009-03, Vol.52 (1), p.3-8 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
|---|---|
| ISSN: | 0008-4395 1496-4287 |
| DOI: | 10.4153/CMB-2009-001-7 |