A Lower Bound for $\tau(n)$ for $k$-Multiperfect Number

Abstract

A natural number $n$ is said to be $k$- multiperfect number if $\sigma (n) = k\cdot n$ for some integer $k>2$. In this paper, I will provide a lower bound for $\tau(n)$ of any $k$- multiperfect numbers. The lower bound for $\tau(n)$ will help in distinguishing if the number is $k$-multiperfect or not.