Journal of Integer Sequences, Vol. 16 (2013), Article 13.7.5

Extremal Orders of Certain Functions Associated with Regular Integers (mod n)

Brăduţ Apostol
"Spiru Haret" Pedagogical High School
1 Timotei Cipariu St.
RO — 620004 Focşani

Lucian Petrescu
“Henri Coandă” Technical College
2 Tineretului St.
RO — 820235 Tulcea


Let V(n) denote the number of positive regular integers (mod n) that are ≤ n, and let Vk(n) be a multidimensional generalization of the arithmetic function V(n). We find the Dirichlet series of Vk(n) and give the extremal orders of some totients involving arithmetic functions which generalize the sum-of-divisors function and the Dedekind function. We also give the extremal orders of other totients regarding arithmetic func- tions which generalize the sum of the unitary divisors of n and the unitary function corresponding to φ(n), the Euler function. Finally, we study extremal orders of some compositions, involving the functions mentioned previously.

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(Concerned with sequences A000010 A000203 A055653 A143869.)

Received April 25 2013; revised version received July 9 2013; July 30 2013; August 5 2013. Published in Journal of Integer Sequences, August 8 2013.

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