Extremal orders of some functions connected to regular integers modulo n

Abstract

Abstract Let V (n) denote the number of positive regular integers (mod n) less than or equal to n. We give extremal orders of , , , , where σ(n), ψ(n) are the sum-of-divisors function and the Dedekind function, respectively. We also give extremal orders for and , where σ*(n) and Φ*(n) represent the sum of the unitary divisors of n and the unitary function corresponding to Φ(n), the Euler's function. Finally, we study some extremal orders of compositions f(g(n)), involving the functions from above.