Square-free values of the Carmichael function

We obtain an asymptotic formula for the number of square-free values among p−1, for primes p x, and we apply it to derive the following asymptotic formula for L(x), the number of square-free values of the Carmichael function λ(n) for 1 n x, where α=0.37395… is the Artin constant, and κ=0.80328… is another absolute constant.