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Odd triperfect numbers are divisible by twelve distinct prime factors

Published online by Cambridge University Press:  09 April 2009

Masao Kishore
Affiliation:
Department of Mathematics East Carolina UniversityGreenville, NC 27834, U.S.A.
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Abstract

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We prove that an odd triperfect number has at least twelve distinct prime factors.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Alexander, L. B., Odd triperfect numbers are bounded below by 1060 (M. A. Thesis, East Carolina University, 1984).Google Scholar
[2]Beck, W. E. and Najar, R. M., “A lower bound for odd triperfecta”, Math. Comp. 38 (1982), 249251.CrossRefGoogle Scholar
[3]Bugulov, E. A., “On the question of the existence of odd multiperfect numbers” (in Russian), Kabardino–Balkarsk. Gos. Univ. Ucen. Zap. 30 (1966), 919.Google Scholar
[4]Cohen, G. L., “On odd perfect numbers II, multiperfect numbers and quasiperfect numbers”, J. Austral. Math. Soc. 29 (1980), 369384.Google Scholar
[5]Cohen, G. L. and Hagis, P. Jr, Results concerning odd multiperfect numbers, to appear.Google Scholar
[6]Kishore, M., “Odd triperfect numbers”, Math. Comp. 42 (1984), 231233.Google Scholar
[7]Kishore, M., “Odd triperfect numbers are divisible by eleven distinct prime factors”, Math. Comp. 44 (1985), 261263.Google Scholar
[8]McDaniel, W., “On odd multiply perfect numbers”, Boll. Un. Mat. Ital. (1970), 185190.Google Scholar
[9]Pomerance, C., “Odd perfect numbers are divisible by at least seven distinct primes”, Acta Arith. 35 (1973/1974), 265300.Google Scholar
[10]Reidlinger, H., “Über ungerademehrfach vollkommene Zahlen”, Osterreichische Akad. Wiss. Math.-Natur. 192 (1983), 237266.Google Scholar