Consider a number divided by the sum of its (base ten) digits. If it goes evenly, repeat the procedure with the quotient. Continue thus until either the quotient arrived at is not evenly divisible by the sum of its digits, or the number 1 is reached.

There are only a finite number of positive integers that reach 1, the largest being 108446423039535872993215143801708248788897518439196551865815224471960229150134987551824227831682497439642537447219998905173574636075570938726770415637566547495970738297545359694233469258248066044412311789418336202690430748419494353337428921317543676766009509734177677473770421445221936204214282140014849868367338680549949846121648321743392211378370176998833209921206655217464739831625543921041252648766408996885700710913879052486492812317563281491911243925427378877369142768640406323066824797472131147967140977568412789256710759050409656222035706522393291677890231411695839455220245836396027648440861440543344125146667943578032458072195974008992176685068654594958348314899096787905903269227303672466102253350452074656943436672832591933669507219965857301188944026241623994044261445035477186928141071384209363011062866156003328225359218417581786664993612723261535530033504534359456197194706824538502279255382972206034525278814354951808365156295137852239659582806470869382588169461649156300693104208166972689007486529034860083473459976647843779025561266682409926743436435548435186073490637074087381530918243621501901195914047236424084375593247227970958601139272341797395550196589930052572977357562548306987001964447384676858917584692194740403103300719776568071910636020311087045555588606644758684325277244510326965842198914723217408000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.
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