#### Vol. 8, No. 8, 2014

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The image of Carmichael's $\lambda$-function

### Kevin Ford, Florian Luca and Carl Pomerance

Vol. 8 (2014), No. 8, 2009–2026
##### Abstract

We show that the counting function of the set of values of Carmichael’s $\lambda$-function is $x∕{\left(logx\right)}^{\eta +o\left(1\right)}$, where $\eta =1-\left(1+loglog2\right)∕\left(log2\right)=0.08607\dots \phantom{\rule{0.3em}{0ex}}$.

##### Keywords
Carmichael's function, Carmichael's lambda function
##### Mathematical Subject Classification 2010
Primary: 11N64
Secondary: 11A25, 11N25