Finite connected components of the aliquot graph

Andrew R. Booker

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arXiv · 1610.07471

Finite connected components of the aliquot graph

Andrew R. Booker

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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 $10^9$, 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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Andrew R. Booker. 2016-10-24. Finite connected components of the aliquot graph. https://arxiv.org/abs/1610.07471

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