Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Breeding amicable numbers in abundance. II

Authors: Stefan Battiato and Walter Borho
Journal: Math. Comp. 70 (2001), 1329-1333
MSC (2000): Primary 11A25
Published electronically: October 17, 2000
MathSciNet review: 1826584
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In a first article of this title, new procedures were described to compute many amicable numbers by ``breeding'' them in several generations. An extensive computer search was later performed (in 1988), and demonstrated the remarkable effectiveness of this breeding method: the number of known amicable pairs was easily quadrupled by this search. As we learnt recently (1999) from the internet, Pederson and te Riele have again multiplied that number roughly by ten. While they give no information on their method of search, we publish here our method and summarize the computations. Our results provide some evidence for the conjecture that the number of amicable pairs is infinite.

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

  • 1. Battiato, S.: Über die Produktion von 37803 neuen befreundeten Zahlenpaaren mit der Brütermethode, Diplom-Arbeit Wuppertal 1988 (unpublished).
  • 2. Borho, W. and Hoffmann, H.: Breeding amicable numbers in abundance, Math. Comp. 46 (1986), 281-293. MR 87c:11003
  • 3. te Riele, H. Table of amicable pairs between $10^{10}$ and $10^{52}$, Centrum voor Wiskunde en Informatica, Note NM-N8GO3, Sept. 1986.
  • 4. Battiato, S. and Borho, W.: Are there odd amicable numbers not divisible by three, Math. Comp. 50 (1988), 633-637. MR 89c:11015
  • 5. Lee, E. J.: Amicable numbers and the bilinear diophantine equation, Math. Comp. 22 (1968), 181-187. MR 37:142

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11A25

Retrieve articles in all journals with MSC (2000): 11A25

Additional Information

Stefan Battiato
Affiliation: Sudermannstr. 2a, 40721 Hilden, Germany

Walter Borho
Affiliation: BUGH FB7, Gaußstraße 20, 42097 Wuppertal, Germany

Received by editor(s): August 25, 1999
Published electronically: October 17, 2000
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society