Are there odd amicable numbers not divisible by three?

Authors:
S. Battiato and W. Borho

Journal:
Math. Comp. **50** (1988), 633-637

MSC:
Primary 11A51

DOI:
https://doi.org/10.1090/S0025-5718-1988-0929559-5

MathSciNet review:
929559

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A conjecture of Bratley and McKay, according to which odd amicable numbers should be divisible by three, is disproved by some counterexamples.

**[1]**W. Borho, "Befreundete Zahlen," in*Lebendige Zahlen*, Math. Miniaturen, vol. 1, Birkhäuser, Basel, 1981.**[2]**W. Borho and H. Hoffmann,*Breeding amicable numbers in abundance*, Math. Comp.**46**(1986), no. 173, 281–293. MR**815849**, https://doi.org/10.1090/S0025-5718-1986-0815849-1**[3]**Paul Bratley and John McKay,*More amicable numbers*, Math. Comp.**22**(1968), 677–678. MR**0225706**, https://doi.org/10.1090/S0025-5718-1968-0225706-9**[4]**Richard K. Guy,*Unsolved problems in number theory*, Unsolved Problems in Intuitive Mathematics, vol. 1, Springer-Verlag, New York-Berlin, 1981. Problem Books in Mathematics. MR**656313****[5]**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.**[6]**Herman J. J. te Riele,*On generating new amicable pairs from given amicable pairs*, Math. Comp.**42**(1984), no. 165, 219–223. MR**725997**, https://doi.org/10.1090/S0025-5718-1984-0725997-0**[7]**H. J. J. te Riele, W. Borho, S. Battiato, H. Hoffmann & E. J. Lee,*Table of Amicable Pairs between**and*, Centrum voor Wiskunde en Informatica, Note NM-N8603, Stichting Math. Centrum, Amsterdam, 1986.**[8]**H. J. J. te Riele,*Computation of all the amicable pairs below 10¹⁰*, Math. Comp.**47**(1986), no. 175, 361–368, S9–S40. With a supplement. MR**842142**, https://doi.org/10.1090/S0025-5718-1986-0842142-3

Retrieve articles in *Mathematics of Computation*
with MSC:
11A51

Retrieve articles in all journals with MSC: 11A51

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0929559-5

Article copyright:
© Copyright 1988
American Mathematical Society