Square-free values of the Carmichael function

[摘要] We obtain an asymptotic formula for the number of square-free values among p - 1, for primes p less than or equal to x, and we apply it to derive the following asymptotic formula for L(x), the number of square-free values of the Carmichael function lambda(n) for 1 less than or equal to n less than or equal to x, L(x) = (kappa + o(1)) x/ln1-alpha x' where alpha = 0.37395... is the Artin constant, and kappa = 0.80328... is another absolute constant. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-11-01

[关键词] square-free integers;Carmichael function;Wirsing theorem