AN UPPER BOUND FOR THE NUMBER OF ODD MULTIPERFECT NUMBERS
AN UPPER BOUND FOR THE NUMBER OF ODD MULTIPERFECT NUMBERS
Abstract A natural number $n$ is called $k$ -perfect if $\sigma (n)= kn$ . In this paper, we show that for any integers $r\geq 2$ and $k\geq 2$ , the number of odd $k$ -perfect numbers $n$ with $\omega (n)\leq r$ is bounded by $\left({\lfloor {4}^{r} { \mathop{ \log } …