Computation of all the amicable pairs below

Author:
H. J. J. te Riele

Journal:
Math. Comp. **47** (1986), 361-368, S9

MSC:
Primary 11A25; Secondary 11Y70

MathSciNet review:
842142

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Abstract: An efficient exhaustive numerical search method for amicable pairs is described. With the aid of this method all 1427 amicable pairs with smaller member below have been computed, more than 800 pairs being new. This extends previous exhaustive work below by H. Cohen. In three appendices (contained in the supplements section of this issue), various statistics are given, including an ordered list of all the gcd's of the 1427 amicable pairs below (which may be useful in further amicable pair research). Suggested by the numerical results, a theorem of Borho and Hoffmann for constructing APs has been extended.

**[1]**W. Borho and H. Hoffmann,*Breeding amicable numbers in abundance*, Math. Comp.**46**(1986), no. 173, 281–293. MR**815849**, 10.1090/S0025-5718-1986-0815849-1**[2]**W. Borho, H. Hoffmann & H. J. J. te Riele,*Table of Amicable Pairs Between**and*, CWI-report. (In preparation.)**[3]**Paul Bratley, Fred Lunnon, and John McKay,*Amicable numbers and their distribution*, Math. Comp.**24**(1970), 431–432. MR**0271005**, 10.1090/S0025-5718-1970-0271005-8**[4]**Henri Cohen,*On amicable and sociable numbers*, Math. Comp.**24**(1970), 423–429. MR**0271004**, 10.1090/S0025-5718-1970-0271004-6**[5]**Elvin Lee,*On divisibility by nine of the sums of even amicable pairs*, Math. Comp.**23**(1969), 545–548. MR**0248074**, 10.1090/S0025-5718-1969-0248074-6**[6]**E. J. Lee & J. S. Madachy, "The history and discovery of amicable numbers,"*J. Recreational Math.*, v. 5, 1972; Part I: pp. 77-93, Part II: pp. 153-173, Part III: pp. 231-249.**[7]**H. J. J. te Riele,*Table of*1869*New Amicable Pairs Generated from*1575*Mother Pairs*, Report NN 27/82, Math. Centre, Amsterdam, Oct. 1982.**[8]**Herman J. J. te Riele,*On generating new amicable pairs from given amicable pairs*, Math. Comp.**42**(1984), no. 165, 219–223. MR**725997**, 10.1090/S0025-5718-1984-0725997-0**[9]**H. J. J. te Riele,*Further Results on Unitary Aliquot Sequences*, Report NW 2/78, Math. Centre, Amsterdam, 2nd ed., Jan. 1978.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1986-0842142-3

Keywords:
Amicable pair

Article copyright:
© Copyright 1986
American Mathematical Society