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Some results concerning quasiperfect numbers

  • Peter Hagis (a1) and Graeme L. Cohen (a2)
Abstract
Abstract

New methods are introduced here to show that if n is a quasiperfect number and ω(n) the number of its distinct prime factors, then ω(n) ≥ 7 and n > 1035, and if further 3 ∤ n then ω(n) ≥ 9 and n > 1040.

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Linked references
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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.

L. Dickson (1913), ‘Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors’, Amer. J. Math. 35, 413422.

R. P. Jerrard and Nicholas Temperley (1973), ‘Almost perfect numbers’, Math. Mag. 46, 8487.

Masao Kishore (1978), ‘Odd integers N with five distinct prime factors for which 2 - 10-12 < σ (N)/N < 2 + 10-12’, Math. Comp. 32, 303309.

C. Pomerance (1975), ‘The second largest prime factor of an odd perfect number’, Math. Comp. 29, 914921.

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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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