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This post is an offshoot of this earlier MSE question.

According to this Wikipedia page:

Grun $1952$ proved that the smallest prime factor $p_1$ (of an odd perfect number $N$) is $< \frac{2\omega(N)}{3} + 2$ (where $\omega(N)$ is the number of distinct prime factors of $N$), and Perisastri $1958$ published the same result.

My question is: Does anybody here know the details of this result of Grun's? I mean, would you be able to reproduce Grun's proof here?

Thanks!

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    $\begingroup$ Otto Grun, Uber ungerade vollkommene Zahlen , Math. Zietschr. 55 (1952) is the name of the paper, I think.. $\endgroup$ – S.C.B. Mar 9 '16 at 9:16

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