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Odd triperfect numbers are divisible by eleven distinct prime factors


Author: Masao Kishore
Journal: Math. Comp. 44 (1985), 261-263
MSC: Primary 11A25
DOI: https://doi.org/10.1090/S0025-5718-1985-0771048-2
MathSciNet review: 771048
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Abstract: We prove that an odd triperfect number has at least eleven distinct prime factors.


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

  • [1] W. E. Beck & R. M. Najar, "A lower bound for odd triperfects," Math. Comp., v. 38, 1982, pp. 249-251. MR 637303 (83m:10006)
  • [2] G. L. Cohen, "On odd perfect numbers II, Multiperfect numbers and quasiperfect numbers," J. Austral. Math. Soc., v. 29, 1980, pp. 369-384. MR 569525 (81m:10009)
  • [3] M. Kishore, "Odd triperfect numbers," Math. Comp., v. 42, 1984, pp. 231-233. MR 725999 (85d:11009)
  • [4] W. McDaniel, "On odd multiply perfect numbers," Boll. Un. Mat. Ital. (4), v. 3, 1970, pp. 185-190. MR 0262154 (41:6764)
  • [5] C. Pomerance, "Odd perfect numbers are divisible by at least seven distinct primes," Acta Arith., v. 25, 1973/1974, pp. 265-300. MR 0340169 (49:4925)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1985-0771048-2
Article copyright: © Copyright 1985 American Mathematical Society

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