Abstract

In this paper, we prove that there are infinitely many [Formula: see text]’s for which [Formula: see text] but [Formula: see text] is not a Carmichael number. Additionally, we prove that for any [Formula: see text], there exist infinitely many [Formula: see text]’s such that [Formula: see text] but [Formula: see text]. The constructions that we consider here are generalizations of Carmichael and Lehmer numbers, respectively, that were first formulated by Grau and Oller-Marcén.

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