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.
Catalan's Aliquot Sequence Conjecture
See also
Aliquot Sequence, Sociable NumbersExplore with Wolfram|Alpha
References
Creyaufmüller, W. "Aliquot Sequences." http://www.aliquot.de/aliquote.htm.Referenced on Wolfram|Alpha
Catalan's Aliquot Sequence ConjectureCite this as:
Weisstein, Eric W. "Catalan's Aliquot Sequence Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatalansAliquotSequenceConjecture.html