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Odd triperfect numbers are divisible by twelve distinct prime factors. (English) Zbl 0612.10006
The positive integer N is said to be a triperfect number if $\sigma (N)=3N$, where $\sigma$ (N) denotes the sum of the positive divisors of N. Although six even triperfect numbers have been found to date, whether or not any odd triperfect numbers exist is an open question. In the present paper it is proved that every odd triperfect number has at least twelve distinct prime factors. This result was obtained earlier by {\it H. Reidlinger} [Sitzungsber., Abt. II, Ă–sterr. Akad. Wiss., Math.- Naturwiss. Kl. 192, 237-266 (1983; Zbl 0553.10007)].
Reviewer: P.Hagis

11A25Arithmetic functions, etc.