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Carmichael’s lambda function. (English) Zbl 0734.11047

Let λ(·) be Carmichael’s function, i.e. λ(n) equals the l.c.m of the orders of primitive residues mod n. Using a more explicit representation via Euler’s function the authors investigate the average order, normal order, and minimal order of λ. For example they show that for x16

1 x nx λ(n)=x logxexp{Bloglogx logloglogx(1+o(1))}

holds with some explicit constant B. Some other problems connected with Euler’s function are discussed.

11N37Asymptotic results on arithmetic functions
11A07Congruences; primitive roots; residue systems
11N45Asymptotic results on counting functions for other structures