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Thursday, August 29, 2013

**Abstract:** Let $\lambda(n)$ denote the maximal order of an element of the group $(\mathbb{Z}/n\mathbb{Z})^*$, commonly called Carmichael's function. We will survey some results about the distribution of values of $\lambda(n)$ and present new, sharp estimates for the counting function of distinct values taken by $\lambda$ (joint with F. Luca and C. Pomerance).