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New amicable four-cycles


Authors: Karsten Blankenagel, Walter Borho and Axel vom Stein
Journal: Math. Comp. 72 (2003), 2071-2076
MSC (2000): Primary 11A25
DOI: https://doi.org/10.1090/S0025-5718-03-01489-3
Published electronically: February 3, 2003
MathSciNet review: 1986823
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Abstract | References | Similar Articles | Additional Information

Abstract: Fifty new amicable four-cycles are discovered by the constructive method invented in 1969 by the second author.


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

  • 1. S. Battiato and W. Borho, Breeding amicable numbers in abundance II, Math. Comp. 70, (2001), 1329-1333. MR 2002b:11011
  • 2. M. Beeler, R. W. Gosper and R. Schroeppel, M.I.T. Artificial Intelligence Memo #239, (29.02.72), Item 61.
  • 3. W. Borho, Über die Fixpunkte der $k$-fach iterierten Teilersummenfunktion, Mitt. Math. Gesellsch. Hamburg 9, (1969), 34-48. MR 40:7189
  • 4. W. Borho and H. Hoffmann, Breeding amicable numbers in abundance, Math. Comp. 46, (1986), 281-293. MR 87c:11003
  • 5. H. Cohen, On amicable and sociable numbers, Math. Comp. 24, (1970), 423-429. MR 42:5887
  • 6. 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), 177-204. MR 80d:10001
  • 7. A. Flammenkamp, New sociable numbers, Math. Comp. 56, (1991), 871-873. MR 92a:11004
  • 8. D. Moews and P. C. Moews, A search for aliquot cycles below $10^{10}$, Math. Comp. 57, (1991), 849-855. MR 92e:11151
  • 9. D. Moews and P. C. Moews, A search for aliquot cycles and amicable pairs, Math. Comp. 61, (1993), 935-938. MR 94a:11198
  • 10. Ren Yuanhua, On constructing sociable numbers, (1990), preprint.

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Additional Information

Karsten Blankenagel
Affiliation: Karsten Blankenagel, BUGH FB 7, Gaußstraße 20, 42097 Wuppertal, Germany
Email: kblanken@math.uni-wuppertal.de

Walter Borho
Affiliation: Walter Borho, BUGH FB 7, Gaußstraße 20, 42097 Wuppertal, Germany
Email: Walter.Borho@math.uni-wuppertal.de

Axel vom Stein
Affiliation: Axel vom Stein, BUGH FB 7, Gaußstraße 20, 42097 Wuppertal, Germany
Email: vomstein@uni-wuppertal.de

DOI: https://doi.org/10.1090/S0025-5718-03-01489-3
Keywords: Number theory, sociable numbers.
Received by editor(s): September 19, 2001
Received by editor(s) in revised form: February 18, 2002
Published electronically: February 3, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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