On the Components of an Odd Perfect Number

If $N=p^k{m}^2$ is an odd perfect number with special prime factor $p$, then it is proved that $p^k<(2\mathrm{/}3)m^2$. Numerical results on the abundancy indices $\frac{\sigma (p^k)}{p^k}$ and $\frac{\sigma (m^2)}{m^2}$, and the ratios $\frac{\sigma (p^k)}{m^2}$ and $\frac{\sigma (m^2)}{p^k}$, are used. It is also showed that $m^2>\frac{\sqrt{6}}{2}({10}^{150})$.