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Sketch of a proof that an odd perfect number relatively prime to $ 3$ has at least eleven prime factors


Author: Peter Hagis
Journal: Math. Comp. 40 (1983), 399-404
MSC: Primary 11A25; Secondary 11-04
DOI: https://doi.org/10.1090/S0025-5718-1983-0679455-1
MathSciNet review: 679455
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Abstract: An argument is outlined which demonstates that every odd perfect number which is not divisible by 3 has at least eleven distinct prime factors.


References [Enhancements On Off] (What's this?)

  • [1] P. Hagis, Jr., "Outline of a proof that every odd perfect number has at least eight prime factors," Math. Comp., v. 35, 1980, pp. 1027-1032. MR 572873 (81k:10004)
  • [2] P. Hagis, Jr., "On the second largest prime divisor of an odd perfect number," Analytic Number Theory, Lecture Notes in Math., vol. 899, Springer-Verlag, Berlin and New York, 1981, pp. 254-263. MR 654532 (83i:10004)
  • [3] P. Hagis, Jr., "Every odd perfect number not divisible by 3 has at least eleven distinct prime factors." (Copy deposited in UMT file.)
  • [4] P. Hagis, Jr. & W. L. McDaniel, "On the largest prime divisor of an odd perfect number. II," Math. Comp., v. 29, 1975, pp. 922-924. MR 0371804 (51:8021)
  • [5] R. P. Jerrard & N. Temperley, "Almost perfect numbers," Math. Mag., v. 46, 1973, pp. 84-87. MR 0376511 (51:12686)
  • [6] M. Kishore, "Odd perfect numbers not divisible by 3 are divisible by at least ten distinct primes," Math. Comp., v. 31, 1977, pp. 274-279. MR 0429716 (55:2727)
  • [7] W. L. McDaniel, "On multiple prime divisors of cyclotomic polynomials," Math. Comp., v. 28, 1974, pp. 847-850. MR 0387177 (52:8022)
  • [8] C. Pomerance, "Odd perfect numbers are divisible by at least seven distinct primes," Acta Arith., v. 25, 1974, pp. 265-300. MR 0340169 (49:4925)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0679455-1
Article copyright: © Copyright 1983 American Mathematical Society

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