On the counting function of the range of the Carmichael $\lambda$-function

The Carmichael $\lambda$-function associates to $n$ the exponent $\lambda(n)$ of the multiplicative group modulo $n$. In my talk, I will describe the main ideas behind the proof that the counting function $\#\{\lambda(n)\le x\}$ of the range of the Carmichael function $\lambda(n)$ below $x$ is $x/(\log x)^{\eta+o(1)}$ as $x\to\infty$, where $\eta=1-(1+\log\log 2)/\log 2=0.08607\ldots$ is the Erdős-Tenebaum-Ford constant. The proof uses sieve methods. This is joint work with Kevin Ford and Carl Pomerance.