Are there odd amicable numbers not divisible by three?
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- by S. Battiato and W. Borho PDF
- Math. Comp. 50 (1988), 633-637 Request permission
Abstract:
A conjecture of Bratley and McKay, according to which odd amicable numbers should be divisible by three, is disproved by some counterexamples.References
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W. Borho, "Befreundete Zahlen," in Lebendige Zahlen, Math. Miniaturen, vol. 1, Birkhäuser, Basel, 1981.
- W. Borho and H. Hoffmann, Breeding amicable numbers in abundance, Math. Comp. 46 (1986), no. 173, 281–293. MR 815849, DOI 10.1090/S0025-5718-1986-0815849-1
- Paul Bratley and John McKay, More amicable numbers, Math. Comp. 22 (1968), 677–678. MR 225706, DOI 10.1090/S0025-5718-1968-0225706-9
- Richard K. Guy, Unsolved problems in number theory, Problem Books in Mathematics, Springer-Verlag, New York-Berlin, 1981. MR 656313 E. J. Lee & J. S. Madachy, "The history and discovery of amicable numbers," J. Recreational Math., v. 5, 1972, pp. 77-93, 153-173, 231-249.
- 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 H. J. J. te Riele, W. Borho, S. Battiato, H. Hoffmann & E. J. Lee, Table of Amicable Pairs between ${10^{10}}$ and ${10^{52}}$, Centrum voor Wiskunde en Informatica, Note NM-N8603, Stichting Math. Centrum, Amsterdam, 1986.
- H. J. J. te Riele, Computation of all the amicable pairs below $10^{10}$, Math. Comp. 47 (1986), no. 175, 361–368, S9–S40. With a supplement. MR 842142, DOI 10.1090/S0025-5718-1986-0842142-3
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Math. Comp. 50 (1988), 633-637
- MSC: Primary 11A51
- DOI: https://doi.org/10.1090/S0025-5718-1988-0929559-5
- MathSciNet review: 929559