Extremal orders of some functions connected to regular integers modulo n
نویسنده
چکیده
Let V (n) denote the number of positive regular integers (mod n) less than or equal to n. We give extremal orders of V (n)σ(n) n2 , V (n)ψ(n) n2 , σ(n) V (n) , ψ(n) V (n) , where σ(n), ψ(n) are the sum-of-divisors function and the Dedekind function, respectively. We also give extremal orders for σ∗(n) V (n) and φ∗(n) V (n) , 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.
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