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New amicable four-cycles
Author(s):
Karsten
Blankenagel;
Walter
Borho;
Axel
vom Stein.
Journal:
Math. Comp.
72
(2003),
2071-2076.
MSC (2000):
Primary 11A25
Posted:
February 3, 2003
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Abstract:
Fifty new amicable four-cycles are discovered by the constructive method invented in 1969 by the second author.
References:
-
- 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
-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
, 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, Gauß{}straß{}e 20, 42097 Wuppertal, Germany
Email:
kblanken@math.uni-wuppertal.de
Walter
Borho
Affiliation:
Walter Borho, BUGH FB 7, Gauß{}straß{}e 20, 42097 Wuppertal, Germany
Email:
Walter.Borho@math.uni-wuppertal.de
Axel
vom Stein
Affiliation:
Axel vom Stein, BUGH FB 7, Gauß{}straß{}e 20, 42097 Wuppertal, Germany
Email:
vomstein@uni-wuppertal.de
DOI:
10.1090/S0025-5718-03-01489-3
PII:
S 0025-5718(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
Posted:
February 3, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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