PDF-2M.BENITO,W.CREYAUFMULLER,J.L.VARONA,ANDP.ZIMMERMANNTheCatalan-Dickso

4MBENITOWCREYAUFMULLERJLVARONAANDPZIMMERMANNthiscasewesaythatn1isthemainsequenceandn2isasidesequenceOnlythemainsequencesarestudiedAccordingto1or2tocomputeanaliquotsequencewehavetodec. VARONA Abstract In this paper we describe some advances in the knowledge of the behavior of aliquot sequences starting with a number less than 10000 For some starting values it is shown for the 64257rst time that the sequence terminates The current 602F.F.Dragan,F.V.Fomin,andP.A.GolovachiscalledapathdecompositionandthepathwidthofistheminimumwidthoverallpathdecompositionsofWewillneedthefollowingresultwhichisduetoRobertson,Seymour&Thomas[33].Propo p1sowealsohavethefollowingformulatocompute(n):(n)=pa1+111 p11


pak+1k1 pk1:(2)Now,letussupossen=23
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