Finite connected components of the aliquot graph

Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than 10^9, as well as those containing an amicable pair below 10^{14} or one of the known perfect or sociable cycles below 10^{17}. Along the way we dev...

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Published in:Mathematics of computation 2018-11, Vol.87 (314), p.2891-2902
Main Author: BOOKER, ANDREW R.
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Language:English
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description Conditional on a strong form of the Goldbach conjecture, we determine all finite connected components of the aliquot graph containing a number less than 10^9, as well as those containing an amicable pair below 10^{14} or one of the known perfect or sociable cycles below 10^{17}. 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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title Finite connected components of the aliquot graph
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