Computation of all the amicable pairs below 10¹⁰

te Riele, H. J. J.

doi:10.1090/S0025-5718-1986-0842142-3

Computation of all the amicable pairs below $10^ {10}$
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by H. J. J. te Riele PDF

Math. Comp. 47 (1986), 361-368 Request permission

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 ${10^{10}}$ have been computed, more than 800 pairs being new. This extends previous exhaustive work below ${10^8}$ 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 ${10^{10}}$ (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.

References

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Table of Amicable Pairs Between

and

Paul Bratley, Fred Lunnon, and John McKay, Amicable numbers and their distribution, Math. Comp. 24 (1970), 431–432. MR 271005, DOI 10.1090/S0025-5718-1970-0271005-8
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J. Recreational Math.

Table of

New Amicable Pairs Generated from

Mother Pairs

Herman J. J. te Riele, On generating new amicable pairs from given amicable pairs, Math. Comp. 42 (1984), no. 165, 219–223. MR 725997, DOI 10.1090/S0025-5718-1984-0725997-0

Further Results on Unitary Aliquot Sequences