On generating new amicable pairs from given amicable pairs
Author:
Herman J. J. te Riele
Journal:
Math. Comp. 42 (1984), 219223
MSC:
Primary 11Y11; Secondary 1104, 11A99
MathSciNet review:
725997
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Abstract: Methods are given for constructing new amicable pairs from given amicable pairs. By applying these methods to 1575 "mother" pairs known to the author, 1782 new amicable pairs were generated, so that the average "offspring" of these mother pairs is greater than 1. By a second, much more restricted application of the methods to the 400 smallest "daughter" pairs, 88 new "granddaughter" pairs were generated.
 [1]
Walter
Borho, On Thabit ibn Kurrah’s formula
for amicable numbers, Math. Comp. 26 (1972), 571–578. MR 0313177
(47 #1732), http://dx.doi.org/10.1090/S00255718197203131774
 [2]
W.
Borho, Some large primes and amicable
numbers, Math. Comp. 36
(1981), no. 153, 303–304. MR 595068
(82d:10021), http://dx.doi.org/10.1090/S00255718198105950682
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P. J. Costello, "Amicable pairs of Euler's first form," J. Recreational Math., v. 10, 19771978, pp. 183189.
 [4]
L. Euler, "De numeris amicabilibus," Leonhardi Euleri Opera Omnia, Teubner, Leipzig and Berlin, Ser. I, vol. 2, 1915, pp. 63162.
 [5]
E. J. Lee & J. S. Madachy, "The history and discovery of amicable numbers," J. Recreational Math., v. 5, 1972, part 1 : pp. 7793, part 2: pp. 153173, part 3: pp. 231249.
 [6]
H.
J. J. te Riele, Four large amicable pairs, Math. Comp. 28 (1974), 309–312. MR 0330033
(48 #8372), http://dx.doi.org/10.1090/S00255718197403300338
 [7]
H. J. J. te Riele, Further Results on Unitary Aliquot Sequences, Report NW 2/78, Mathematical Centre, Amsterdam, 2nd ed., Jan. 1978.
 [8]
H. J. J. te Riele, Table of 1870 New Amicable Pairs Generated from 1575 Mother Pairs, Report NN 27/82, Mathematical Centre, Amsterdam, Oct. 1982.
 [9]
D. Woods, "Construction of amicable pairs," Abstracts Amer. Math. Soc., v. 3, 1982, p. 223.
 [10]
D. Woods, "List of 456 new amicable pairs," privately communicated to the author on June 29, 1982.
 [11]
Walter
Borho, Große Primzahlen und befreundete Zahlen: Über den
LucasTest und ThabitRegeln, Mitt. Math. Ges. Hamburg
11 (1983), no. 2, 232–256 (German, with English
summary). In collaboration with J. Buhl, H. Hoffmann, S. Mertens, E. Nebgen
and R. Reckow. MR
744530 (85f:11094)
 [1]
 W. Borho, "On Thabit ibn Kurrah's formula for amicable numbers," Math. Comp., v. 26, 1972, pp. 571578. MR 0313177 (47:1732)
 [2]
 W. Borho, "Some large primes and amicable numbers," Math. Comp., v. 36, 1981, pp. 303304. MR 595068 (82d:10021)
 [3]
 P. J. Costello, "Amicable pairs of Euler's first form," J. Recreational Math., v. 10, 19771978, pp. 183189.
 [4]
 L. Euler, "De numeris amicabilibus," Leonhardi Euleri Opera Omnia, Teubner, Leipzig and Berlin, Ser. I, vol. 2, 1915, pp. 63162.
 [5]
 E. J. Lee & J. S. Madachy, "The history and discovery of amicable numbers," J. Recreational Math., v. 5, 1972, part 1 : pp. 7793, part 2: pp. 153173, part 3: pp. 231249.
 [6]
 H. J. J. te Riele, "Four large amicable pairs," Math. Comp., v. 28, 1974, pp. 309312. MR 0330033 (48:8372)
 [7]
 H. J. J. te Riele, Further Results on Unitary Aliquot Sequences, Report NW 2/78, Mathematical Centre, Amsterdam, 2nd ed., Jan. 1978.
 [8]
 H. J. J. te Riele, Table of 1870 New Amicable Pairs Generated from 1575 Mother Pairs, Report NN 27/82, Mathematical Centre, Amsterdam, Oct. 1982.
 [9]
 D. Woods, "Construction of amicable pairs," Abstracts Amer. Math. Soc., v. 3, 1982, p. 223.
 [10]
 D. Woods, "List of 456 new amicable pairs," privately communicated to the author on June 29, 1982.
 [11]
 W. Borho, "Grosse Primzahlen und befreundete Zahlen: über den LucasTest und ThabitRegeln," Mitt. Math. Ges. Hamburg. (To appear.) MR 744530 (85f:11094)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198407259970
PII:
S 00255718(1984)07259970
Keywords:
Amicable pair
Article copyright:
© Copyright 1984
American Mathematical Society
