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.

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