Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Breeding amicable numbers in abundance. II

Author(s): Stefan Battiato; Walter Borho.
Journal: Math. Comp. 70 (2001), 1329-1333.
MSC (2000): Primary 11A25
Posted: October 17, 2000
MathSciNet review: 1826584
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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:

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S.: Über die Produktion von 37803 neuen befreundeten Zahlenpaaren mit der Brütermethode, Diplom-Arbeit Wuppertal 1988 (unpublished).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. et.al: 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

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