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Finite connected components of the aliquot graph

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)2891-2902
Number of pages12
JournalMathematics of Computation
Issue number314
Early online date20 Feb 2018
DateAccepted/In press - 14 Jun 2017
DateE-pub ahead of print - 20 Feb 2018
DatePublished (current) - 2018


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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