Pappalardi, Francesco Square free values of the order function. (English) Zbl 1066.11044 New York J. Math. 9, 331-344 (2003). Summary: Given \(a\in\mathbb{Z}\setminus\{\pm1,0\}\), we consider the problem of enumerating the integers \(m\) coprime to \(a\) such that the order of \(a\) modulo \(m\) is square free. This question is raised in analogy to a result recently proved jointly with F. Saidak and I. Shparlinski where square free values of the Carmichael function are studied. The technique is the one of Hooley that uses the Chebotarev Density Theorem to enumerate primes for which the index \(i_p(a)\) of \(a\) modulo \(p\) is divisible by a given integer. Cited in 6 Documents MSC: 11N37 Asymptotic results on arithmetic functions 11N56 Rate of growth of arithmetic functions Keywords:Square free integers; Carmichael function; Wirsing theorem; Chebotarev density theorem PDFBibTeX XMLCite \textit{F. Pappalardi}, New York J. Math. 9, 331--344 (2003; Zbl 1066.11044) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Odd numbers k such that the multiplicative order of 2 modulo k is squarefree. Numbers k not divisible by 3 such that the multiplicative order of 3 modulo k is squarefree.