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Publication - Dr Andrew Booker

    Finite connected components of the aliquot graph

    Citation

    Booker, AR, 2018, ‘Finite connected components of the aliquot graph’. Mathematics of Computation, vol 87., pp. 2891-2902

    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.

    Full details in the University publications repository