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Publication - Dr Andrew Booker

    Finite connected components of the aliquot graph

    Citation

    Booker, A, 2017, ‘Finite connected components of the aliquot graph’. Mathematics of Computation.

    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.

    Full details in the University publications repository