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, H. Hoffmann, "Breeding amicable numbers in abundance,"*Math. Comp.*, v. 46, 1986, pp. 281-293. MR**815849 (87c:11003)****[3]**P. Bratley & J. McKay, "More amicable numbers,"*Math. Comp.*, v. 22, 1968, pp. 677-678. MR**0225706 (37:1299)****[4]**R. K. Guy,*Unsolved Problems in Number Theory*, Vol 1, Springer-Verlag, New York, Heidelberg, Berlin, 1981, pp. 31-32. MR**656313 (83k:10002)****[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]**H. J. J. te Riele, "On generating new amicable pairs from given amicable pairs,"*Math. Comp.*, v. 42, 1984, pp. 219-223. MR**725997 (85d:11107)****[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 ,"*Math. Comp.*, v. 47, 1986, pp. 361-368. MR**842142 (87i:11014)**

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