For info on the behavior of aliquot sequences, see Richard K.~Guy \& J.~L.~Selfridge, What drives an aliquot sequence? {\it Math.\ Comput.}, {\bf 29}(1975) 101--107; {\it MR} {\bf 52} \#5542. For the latest I have on 46758 or 99225 [assuming I've made no errors] see the following, where %x shoud be read as s^{758+x)(99225) = s^{759+x}(46758} and s(n) = sigma(n) - n. The max so far is x = 10 with 109 decimal digits. It is presently equipped with a down-dribbler, 2^2 without 7. x = 18 will have only 108 digits. What are p and q ? %10 = 2634352957536601215651504310367034664237525994841454140912074056001634101746270450889034819192963235153851324 ? sigma(%10)-%10 %11 = 4375257663618965969838703886908135210362400648826184831403998005722029284842736914906603629552172468620027076 ? sigma(%11)-%11 %12 = 3812107258892467560724974268427776342559095577235276386026267812986314208130577642999593014216712259224932924 ? sigma(%12)-%12 %13 = 3357281129948365843366244433222476932983757953562658831902107291213172363666597435003856377831158249456856516 ? sigma(%13)-%13 %14 = 2518171581657269542751815956477757174750853819031465204680695087344865157789907955347820287620116570491943484 ? sigma(%14)-%14 %15 = 1888629123883173758068189431062891256470513916997092605609774658685559002236728244577771226723234026392998116 ? sigma(%15)-%15 %16 = 1416471844370396313297145002601020142112938329621791431806267389982998189766074091264106125133452654937155868 ? sigma(%16)-%16 %17 = 1062353883280402701838073792504970617432775483305445625911321617689753946299262182125924369941690102569916132 [= 2^2*15178595752127*230389769006487808825024129*p*q] R.