<abstract xmlns="http://www.w3.org/1999/xhtml">We obtain an arithmetic proof and a refinement of the inequality ϕ (<italic>nk</italic>) + σ<italic>k</italic>(<italic>n</italic>) &lt; 2<italic>nk</italic>, where <italic>n</italic> ≧ 2 and <italic>k</italic> ≧ 2. An application to another inequality is also provided.</abstract>

We obtain an arithmetic proof and a refinement of the inequality ϕ (nk) + σk(n) < 2nk, where n ≧ 2 and k ≧ 2. An application to another inequality is also provided.

On an Arithmetic Inequality

Department of Mathematics Babes-Bolyai University 400084 Cluj-Napoca, Romania

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On an Arithmetic Inequality"}

We obtain an arithmetic proof and a refinement of the inequality ϕ (nk) + σk(n) < 2nk, where n ≧ 2 and k ≧ 2. An application to another inequality is also...

On an Arithmetic Inequality

Published Online: Dec 10, 2014

Page range: 257 - 261

Received: Sep 20, 2013

Accepted: Nov 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0021

Keywords
Divisibility, Euler totient, sum of divisors, number of divisors, Dedekind arithmetical function, inequalities

© 2014 József Sándor

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On an Arithmetic Inequality

Published Online: Dec 10, 2014

Page range: 257 - 261

Received: Sep 20, 2013

Accepted: Nov 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0021

KeywordsDivisibility, Euler totient, sum of divisors, number of divisors, Dedekind arithmetical function, inequalities

© 2014 József Sándor

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Divisibility, Euler totient, sum of divisors, number of divisors, Dedekind arithmetical function, inequalities