On the Components of an Odd Perfect Number

Jose Arnaldo B. Dris

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arXiv · 1206.3230

On the Components of an Odd Perfect Number

Jose Arnaldo B. Dris

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Abstract

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

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Jose Arnaldo B. Dris. 2012-06-14. On the Components of an Odd Perfect Number. https://arxiv.org/abs/1206.3230

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