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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The first known type $(7,1)$ amicable pair


Author: Mariano Garcia
Journal: Math. Comp. 72 (2003), 939-940
MSC (2000): Primary 11A25
Published electronically: May 15, 2002
MathSciNet review: 1954976
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Abstract | References | Similar Articles | Additional Information

Abstract: Amicable pairs of type $(i, 1)$ have been the object of special search partly because they breed other amicable pairs. Examples exist for $i=2, 3, 4, 5,$and 6. In this paper we exhibit the first known type $(7,1)$ pair.


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

  • 1. W. Borho and H. Hoffmann, Breeding amicable numbers in abundance, Math. Comp. 46 (1986), 281-293. MR 87c:11003
  • 2. P. Costello, Amicable pairs of the form $(i,1)$, Math. Comp. 56 (1991), 859-865. MR 91k:11009
  • 3. E. B. Escott, Amicable numbers, Scripta Math. 12 (1946), 61-72. MR 8:135a
  • 4. L. Euler, De numeris amicabilibus, Opuscula varii argumenti (1750), 23-107.
  • 5. E. J. Lee and J. S. Madachy, The history and discovery of amicable numbers, J. Recr. Math. 5 (1972), Part 1, 77-93, Part 2, 153-173, Part 3, 231-249. MR 56:5165a; MR 56:5165b; MR 56:5165c; errata MR 56:5165d; errata MR 56:5165e
  • 6. H. J. J. te Riele, On generating new amicable pairs from given amicable pairs, Math. Comp. 42 (1984), 219-223. MR 85d:11107
  • 7. J. Pedersen, Various amicable pair lists and statistics, http://www.vejlehs.dk/staff/ jmp/aliquot/apstat.htm.

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Additional Information

Mariano Garcia
Affiliation: Department of Mathematics, Touro College, 27 West 23rd Street, New York, New York 10010

DOI: http://dx.doi.org/10.1090/S0025-5718-02-01450-3
PII: S 0025-5718(02)01450-3
Keywords: Amicable pairs
Received by editor(s): May 21, 2001
Published electronically: May 15, 2002
Article copyright: © Copyright 2002 American Mathematical Society