denote the number of positive regular integers
less than or equal to
) be the multidimensional generalization of the arithmetic function
. We study the behaviour of the sequence
. We also investigate the average orders of the functions
. 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
, 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,
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