On an Arithmetic Inequality

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.

Keywords

• divisibility
• euler totient
• sum of divisors
• number of divisors
• dedekind arithmetical function
• inequalities