Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T11:07:00.319Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results concerning quasiperfect numbers

Published online by Cambridge University Press:  09 April 2009

Peter Hagis Jr  and
Graeme L. Cohen
Peter Hagis Jr
Affiliation:
Department of Mathematics Temple University Philadelphia, Pennsylvania 19122, U.S.A.
Graeme L. Cohen
Affiliation:
School of Mathematical Sciences The New South Wales Institute of Technology Broadway, New South Wales 2007, Australia
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.

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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 275 - 286
Copyright
Copyright © Australian Mathematical Society 1982

References

Abbott, H. L., Aull, C. E., Brown, Ezra and Suryanarayana, D. (1973), ‘Quasiperfect numbers’, Acta Arith. 22, 439–447:CrossRefGoogle Scholar
(1976), ‘Corrections to the paper “Quasiperfect numbers”‘, Acta Arith. 29, 427–428.CrossRefGoogle Scholar
Cattaneo, Paolo (1951), ‘Sui numeri quasiperfetti’, Boll. Un. Mat. Ital. (3) 6, 59–62.Google Scholar
Dickson, L. (1913), ‘Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors’, Amer. J. Math. 35, 413–422.CrossRefGoogle Scholar
Jerrard, R. P. and Temperley, Nicholas (1973), ‘Almost perfect numbers’, Math. Mag. 46, 84–87.CrossRefGoogle Scholar
Kishore, Masao (1978), ‘Odd integers N with five distinct prime factors for which 2 - 10-12 < σ (N)/N < 2 + 10-12’, Math. Comp. 32, 303–309.Google Scholar
Pomerance, C. (1974). ‘Odd perfect numbers are divisible by at least seven distinct primes’, Acta Arith. 25, 265–300.CrossRefGoogle Scholar
Pomerance, C. (1975), ‘The second largest prime factor of an odd perfect number’, Math. Comp. 29, 914–921.CrossRefGoogle Scholar