The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The conjecture remains open to this day.

Creyaufmüller, W. "Aliquot Sequences." http://www.aliquot.de/aliquote.htm.

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Weisstein, Eric W. "Catalan's Aliquot Sequence Conjecture." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CatalansAliquotSequenceConjecture.html