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Some results concerning quasiperfect numbers

  • Peter Hagis (a1) and Graeme L. Cohen (a2)
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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Copyright
References
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Abbott, H. L., Aull, C. E., Brown, Ezra and Suryanarayana, D. (1973), ‘Quasiperfect numbers’, Acta Arith. 22, 439447:
(1976), ‘Corrections to the paper “Quasiperfect numbers”‘, Acta Arith. 29, 427428.
Cattaneo, Paolo (1951), ‘Sui numeri quasiperfetti’, Boll. Un. Mat. Ital. (3) 6, 5962.
Dickson, L. (1913), ‘Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors’, Amer. J. Math. 35, 413422.
Jerrard, R. P. and Temperley, Nicholas (1973), ‘Almost perfect numbers’, Math. Mag. 46, 8487.
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, 303309.
Pomerance, C. (1974). ‘Odd perfect numbers are divisible by at least seven distinct primes’, Acta Arith. 25, 265300.
Pomerance, C. (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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