Article contents
Odd triperfect numbers are divisible by twelve distinct prime factors
Published online by Cambridge University Press: 09 April 2009
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We prove that an odd triperfect number has at least twelve distinct prime factors.
- Type
- Research Article
- Information
- 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), 249–251.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), 9–19.Google Scholar
[4]Cohen, G. L., “On odd perfect numbers II, multiperfect numbers and quasiperfect numbers”, J. Austral. Math. Soc. 29 (1980), 369–384.Google Scholar
[5]Cohen, G. L. and Hagis, P. Jr, Results concerning odd multiperfect numbers, to appear.Google Scholar
[7]Kishore, M., “Odd triperfect numbers are divisible by eleven distinct prime factors”, Math. Comp. 44 (1985), 261–263.Google Scholar
[8]McDaniel, W., “On odd multiply perfect numbers”, Boll. Un. Mat. Ital. (1970), 185–190.Google Scholar
[9]Pomerance, C., “Odd perfect numbers are divisible by at least seven distinct primes”, Acta Arith. 35 (1973/1974), 265–300.Google Scholar
[10]Reidlinger, H., “Über ungerademehrfach vollkommene Zahlen”, Osterreichische Akad. Wiss. Math.-Natur. 192 (1983), 237–266.Google Scholar
- 4
- Cited by