Abstract
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, L(x)=(κ+o(1)) x ln 1−α x , where α=0.37395… is the Artin constant, and κ=0.80328… is another absolute constant.
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