## Bradut Apostol: Asymptotic properties of some functions related to regular integers modulo n, 221-231

### Abstract:

Let denote the number of positive regular integers less than or equal to and let () be the multidimensional generalization of the arithmetic function . We study the behaviour of the sequence . We also investigate the average orders of the functions , and . Here the functions , , generalize the Dedekind function, the sum of the divisors of and the sum of the unitary divisors of , respectively. Finally, we give the extremal orders of some compositions involving the functions mentioned previously and the functions and which generalize , the Euler function and the unitary function corresponding to .

Key Words: arithmetical function, composition, regular integers , average orders, extremal orders.

2010 Mathematics Subject Classification: Primary 11A25,
Secondary 11N37

Download the paper in pdf format here.