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    TANG, MIN and FENG, MIN 2014. ON DEFICIENT-PERFECT NUMBERS. Bulletin of the Australian Mathematical Society, Vol. 90, Issue. 02, p. 186.


    Kishore, Masao 1987. Odd triperfect numbers are divisible by twelve distinct prime factors. Journal of the Australian Mathematical Society, Vol. 42, Issue. 02, p. 173.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 29, Issue 3
  • May 1980, pp. 369-384

On odd perfect numbers (II), multiperfect numbers and quasiperfect numbers

  • Graeme L. Cohen (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788700021376
  • Published online: 01 April 2009
Abstract

Let N be a positive integer. This paper is concerned with obtaining bounds for (p prime), when N is an odd perfect number, a multiperfect number, or a quasiperfect number, under assumptions on the existence of such numbers (where none is known) and whether 3 and 5 are divisors. We argue that our new lower bounds in the case of odd perfect numbers are not likely to be significantly improved further. Triperfect numbers are investigated in some detail, and it is shown that an odd triperfect number must have at least nine distinct prime factors.

1980 Mathematics subject classification (Amer. Math. Soc.): 10 A 20.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

Masao Kishore (1978), 'Odd integers N with five distinct prime factors for which 2–10–12Math. Comp. 32, 303309.

D. Suryanarayana (1963), 'On odd perfect numbers II', Proc. Amer. Math. Soc. 14, 896904.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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