On generating new amicable pairs from given amicable pairs

Author:
Herman J. J. te Riele

Journal:
Math. Comp. **42** (1984), 219-223

MSC:
Primary 11Y11; Secondary 11-04, 11A99

DOI:
https://doi.org/10.1090/S0025-5718-1984-0725997-0

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.

- Walter Borho,
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*Some large primes and amicable numbers*, Math. Comp.**36**(1981), no. 153, 303–304. MR**595068**, DOI https://doi.org/10.1090/S0025-5718-1981-0595068-2
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H. J. J. te Riele, - Walter Borho,
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*Table of*1870

*New Amicable Pairs Generated from*1575

*Mother Pairs*, Report NN 27/82, Mathematical Centre, Amsterdam, Oct. 1982. D. Woods, "Construction of amicable pairs,"

*Abstracts Amer. Math. Soc.*, v. 3, 1982, p. 223. D. Woods, "List of 456 new amicable pairs," privately communicated to the author on June 29, 1982.

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Additional Information

Keywords:
Amicable pair

Article copyright:
© Copyright 1984
American Mathematical Society