Lower bounds on expressions dependent on functions $\varphi(n)$, $\psi(n)$ and $\sigma(n)$, II

TL;DR

This paper establishes lower bounds on various mathematical expressions involving the functions (n), (n), and (n), providing theoretical insights into their behavior.

Contribution

It introduces new lower bounds for expressions dependent on (n), (n), and (n), advancing understanding of these functions' properties.

Findings

Derived new lower bounds for (n), (n), and (n) expressions.

Enhanced theoretical understanding of the relationships between these functions.

Provided mathematical proofs supporting the bounds.

Abstract

In this paper we establish lower bounds on several expressions dependent on functions $\varphi(n)$, $\psi(n)$ and $\sigma(n)$.