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

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Brăduţ Apostol

"Spiru Haret" Pedagogical High School

1 Timotei Cipariu St.

RO — 620004 Focşani

Romania

Lucian Petrescu

“Henri Coandă” Technical College

2 Tineretului St.

RO — 820235 Tulcea

Romania

**Abstract:**

Let *V*(*n*) denote the number of positive regular integers
(mod *n*) that
are ≤ *n*, and let *V*_{k}(*n*)
be a multidimensional generalization of the
arithmetic function *V*(*n*).
We find the Dirichlet series of *V*_{k}(*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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