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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Advances in aliquot sequences


Authors: Manuel Benito and Juan L. Varona
Journal: Math. Comp. 68 (1999), 389-393
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 $10000$. 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/S0025-5718-99-00991-6
PII: S 0025-5718(99)00991-6
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 PB93-0228-C02-02 of the DGICYT
Article copyright: © Copyright 1999 American Mathematical Society