Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T23:02:49.145Z Has data issue: false hasContentIssue false
  • English
  • Français

Odd triperfect numbers are divisible by twelve distinct prime factors

Published online by Cambridge University Press:  09 April 2009

Masao Kishore
Masao Kishore
Affiliation:
Department of Mathematics East Carolina UniversityGreenville, NC 27834, U.S.A.
Rights & Permissions [Opens in a new window]

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
Journal of the Australian Mathematical Society , Volume 42 , Issue 2 , April 1987 , pp. 173 - 182
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
[6]Kishore, M., “Odd triperfect numbers”, Math. Comp. 42 (1984), 231–233.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