Extremal Orders of Certain Functions Associated with
Regular Integers (mod n)
"Spiru Haret" Pedagogical High School
1 Timotei Cipariu St.
RO — 620004 Focşani
“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.
Full version: pdf,
(Concerned with sequences
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.
Journal of Integer Sequences home page