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Carmichael Numbers with a Square Totient

  • W. D. Banks
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Abstract

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 $\varphi(n)$ is a perfect square. We also obtain similar results for higher powers.
MSC Classifications: 11N25, 11A25 show english descriptions Distribution of integers with specified multiplicative constraints
Arithmetic functions; related numbers; inversion formulas
11N25 - Distribution of integers with specified multiplicative constraints
11A25 - Arithmetic functions; related numbers; inversion formulas
 

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