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A search for aliquot cycles below $ 10\sp {10}$


Authors: David Moews and Paul C. Moews
Journal: Math. Comp. 57 (1991), 849-855
MSC: Primary 11Y55; Secondary 11B83
DOI: https://doi.org/10.1090/S0025-5718-1991-1094955-5
MathSciNet review: 1094955
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Abstract | References | Similar Articles | Additional Information

Abstract: A search for aliquot k-cycles below $ {10^{10}}$ with $ k \geq 3$ is described. Two new 4-cycles are exhibited. Six new 4-cycles not below $ {10^{10}}$ are also exhibited.


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

  • [1] Walter Borho, Über die Fixpunkte der k-fach iterierten Teilersummenfunktion, Mitt. Math. Gesellsch. Hamburg 9 (1969), 34-48. MR 0253976 (40:7189)
  • [2] Henri Cohen, On amicable and sociable numbers, Math. Comp. 24 (1970), 423-429. MR 0271004 (42:5887)
  • [3] Patrick J. Costello, Amicable pairs of Euler's first form, J. Recreational Math. 10 (1977-1978), 183-189.
  • [4] J. S. Devitt, R. K. Guy, and J. L. Selfridge, Third report on aliquot sequences, Congr. Numer. XVIII, Proc. 6th Manitoba Conf. Numerical Math. 1976, pp. 177-204. MR 532697 (80d:10001)
  • [5] P. Erdös, On amicable numbers, Publ. Math. Debrecen 4 (1955-1956), 108-111. MR 0069198 (16:998h)
  • [6] -, On asymptotic properties of aliquot sequences, Math. Comp. 30 (1976), 641-645. MR 0404115 (53:7919)
  • [7] A. Flammenkamp, New sociable numbers, Math. Comp. 56 (1991), 871-873. MR 1052094 (92a:11004)
  • [8] P. Poulet, L'intermédiaire des math. 25 (1918), 100-101.
  • [9] H. J. J. te Riele, Computation of all the amicable pairs below $ {10^{10}}$, Math. Comp. 47 (1986), 361-368. MR 842142 (87i:11014)
  • [10] S. C. Root, Item 61, M.I.T. Artificial Intelligence Memo no. 239, Feb. 29, 1972.
  • [11] Charles R. Wall, The density of the abundant numbers, Notices Amer. Math. Soc. 20 (1973), A-472.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1991-1094955-5
Keywords: Amicable numbers, sociable numbers, aliquot cycles
Article copyright: © Copyright 1991 American Mathematical Society

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