Advances in aliquot sequences
Authors:
Manuel Benito and Juan L. Varona
Journal:
Math. Comp. 68 (1999), 389393
MSC (1991):
Primary 11Y55; Secondary 11A25
MathSciNet review:
1489967
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Abstract: In this paper we describe some advances in the knowledge of the behavior of aliquot sequences starting with a number less than . For some starting values, it is shown for the first time that the sequence terminates. The current record for the maximum of a terminating sequence is located in the one starting at 4170; it converges to 1 after 869 iterations getting a maximum of 84 decimal digits at iteration 289.
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Additional Information
Manuel Benito
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain
Email:
mbenito@dmc.unirioja.es
Juan L. Varona
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain
Email:
jvarona@dmc.unirioja.es
DOI:
http://dx.doi.org/10.1090/S0025571899009916
PII:
S 00255718(99)009916
Keywords:
Aliquot sequences,
sum of divisors,
perfect number,
amicable pair,
sociable numbers,
aliquot cycles
Received by editor(s):
October 25, 1996
Received by editor(s) in revised form:
February 26, 1997, and July 24, 1997
Additional Notes:
Research of the second author supported by grant PB930228C0202 of the DGICYT
Article copyright:
© Copyright 1999
American Mathematical Society
