<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Let V (n) denote the number of positive regular integers (mod n) less than or equal to n. We give extremal orders of <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/auom_5_Fig_1.png"></inline-graphic></inline-formula>, <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/auom_5_Fig_2.png"></inline-graphic></inline-formula>, <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/auom_5_Fig_3.png"></inline-graphic></inline-formula>, <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/auom_5_Fig_4.png"></inline-graphic></inline-formula>, where σ(n), ψ(n) are the sum-of-divisors function and the Dedekind function, respectively. We also give extremal orders for <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/auom_5_Fig_5.png"></inline-graphic></inline-formula> and <inline-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/auom_5_Fig_6.png"></inline-graphic></inline-formula>, 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. </p></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.

Extremal orders of some functions connected to regular integers modulo n

"Spiru Haret" Pedagogical High School, 1 Timotei Cipariu St. , RO - 620004 Focşani, ROMANIA

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Extremal orders of some functions connected to regular integers modulo n"}

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...

Extremal orders of some functions connected to regular integers modulo n

Published Online: Sep 19, 2013

Page range: 5 - 19

DOI: https://doi.org/10.2478/auom-2013-0020

Keywords
Arithmetical function, composition, regular integers (mod n), extremal orders

This content is open access.

Extremal orders of some functions connected to regular integers modulo n

Published Online: Sep 19, 2013

Page range: 5 - 19

DOI: https://doi.org/10.2478/auom-2013-0020

KeywordsArithmetical function, composition, regular integers (mod n), extremal orders

This content is open access.

Keywords
Arithmetical function, composition, regular integers (mod n), extremal orders