K-LEHMER AND K-CARMICHAEL NUMBERS

摘要

Grau and Oller-Marcen have defined k-Lehmer and k-Carmichael numbers as generalizations of Lehmer and Carmichael numbers, respectively. We partially resolve some of their conjectures by proving that for infinitely many k there are Carmichael numbers that are k-Lehmer but not (k 1)-Lehmer. We also prove an analogous result for k-Carmichael numbers.