Finite connected components of the aliquot graph

Andrew R. Booker

doi:10.1090/mcom/3299

Finite connected components of the aliquot graph

Andrew R. Booker^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

4 Citations (Scopus)

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Abstract

Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than 10⁹, as well as those containing an amicable pair below 10¹⁴ or one of the known perfect or sociable cycles below 10¹⁷. Along the way we develop a fast algorithm for computing the inverse image of an even number under the sum-of-proper-divisors function.

Original language	English
Pages (from-to)	2891-2902
Number of pages	12
Journal	Mathematics of Computation
Volume	87
Issue number	314
Early online date	20 Feb 2018
DOIs	https://doi.org/10.1090/mcom/3299
Publication status	Published - 2018

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via AMS at http://www.ams.org/journals/mcom/2018-87-314/S0025-5718-2018-03299-9/ . Please refer to any applicable terms of use of the publisher.
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abstract = "Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than 109, as well as those containing an amicable pair below 1014 or one of the known perfect or sociable cycles below 1017. Along the way we develop a fast algorithm for computing the inverse image of an even number under the sum-of-proper-divisors function.",

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AB - Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than 109, as well as those containing an amicable pair below 1014 or one of the known perfect or sociable cycles below 1017. Along the way we develop a fast algorithm for computing the inverse image of an even number under the sum-of-proper-divisors function.

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M3 - Article (Academic Journal)

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Finite connected components of the aliquot graph

Abstract

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