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Multiple Harshad Numbers (Posted on 2016-07-10) Difficulty: 3 of 5
A number is called Harshad if it is divisible by the sum of its digits.
For example 102 is divisible by 3.
This quotient is not Harshad because 34 is not divisible by 7.
108 is a Multiple Harshad Number because the process ends at 1:
108/9=12; 12/3=4; 4/4=1.

Find the Multiple Harshad Numbers below 1000.

Hard bonus: Apparently there are only 15095 of these numbers. Can you prove the list is finite?

No Solution Yet Submitted by Jer    
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re(2): Moby Dick has been captured -- part 2 solved | Comment 11 of 12 |
(In reply to re: Moby Dick has been captured -- part 2 solved by Jer)

The largest has 440 steps, as do the 2nd, 3rd and 4th largest.  All are listed in comment 9 (re: phase 24 output continued) -- (I forgot to take out the "re:"). The number of steps is the 3-digit number preceding the MHN, so you can find in page 440b, where b stands for blank.


or here they are, copied:

 440   101552893979782336754962978028335305584986022229210760017859329338098019107906560166336417183
4926518109623627781939962121664826982460075877770082610464454214663001513398398562780147415029859948
2234952021905957216696631814904652696168274592577360817501400645936659835193776430417595870176957576
7711480811893169566164322102232267917410308546409148856759654127726583204015051126393826544693366941
5786146884288189662807899528389758180233234955892120329142375876227421735833934218686294102809280592
6169707168712766110162310411950683480076193390563687156911739640710467680677856404796563540565935192
1850516256989392802316632347442583319761151588404299551452582392557420634705348362813256549919176122
8009836448688433914624909725554562216569892227560065834893913422057379140909496669483038491307472913
6311552643129799531490328415525327943915478038848017767976846775116175006947051863949006083543005583
7798616894325600071453627300269086878090771274011572064657009944973117722469493972469185469070486545
4245560034235771358355491713766778506794282110879225472147931918860723062480009259769394783562314035
9965709270706837152898257368430381603051706955650536522597611194333123540698023705796882902365295070
0129258078571727223250151469332066797744515617007618403939247405019139858507587129980860884004553323
6980600979817277776579502528350126080000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000

 440   106173593814156378649045964141193405251405654280291234910543647911170643509263894998342881739
4017265352188914528171845568615536107685978951007602572260007815304863216266387204192046240941530466
9617612561419100580323284687045860674712975825530190653383977577749423982195785307728319632676280859
3592170227266335687869879741316412511979670925907547086969696462454024654419928475957859106445695151
1665154090291676096530912240672160571351785264766258917813675557327930925141008543275834360564422418
3648768079417694510440413798486352757330526222935831147551678556488055590306748353849407301946557197
9162160751669681224320240771107834173022778693116588149029992365426800538619676660627680330446219545
8110671120863640653545294027059641205316236824217393078902320023493909611109163247709357083863476811
4410282226485540304657854195535428051636054655462347141590227696563508479328138543575501940918901683
8593548851827041650818232832851179848027950317690149933180744561609928066730857279682512796737504925
3774568864350462517814203570278318006358198949573094566892369701977398314803123901372635671806084627
9569044989719829677153013141750392417841562572408247456126518725166397529444585115241654847713651473
9381126900448031060762842313970210162717605125193950105889035208128077780364447496696639144828850568
1867235298050207120670630093248266240000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000 

 440   107310008426846125821130553971450827020151586359743893388179436191565436329699441275083554785
5421119874307144500185917310175641234220844169137653364317836645132285299620920400567190466762005563
7029421870180467100296163880943905055023359358830972510530289264361420874971581174936420913148351143
7866092538567351513275214845581267080150707159059462728573347647831972930537572970348845365994808096
2095820877190822476769010689731342718139954220199536918463057405800859849416218114839948795616335196
5430941438065896133640846362078714331185745922569700899895503862138539365738166149685715942793079981
3801511096106512674733454357342933315547487333562790162857530510010879443467287878707793116857723424
7417666071698572587145931730713184765617786759644796368737665956467086013674551845161903719317673046
4258710323710920705472234897934125293778948206820506820475750011358530741339295989760560830194792068
8547914053605006928426379055832767399918157736992643892710202072208199468056722724572080976519099014
7928119295620268691552276085556526303062338693681675089779596900622416339579304126616685289088412750
8861068407040989933636302273237017413139560948565522275993316326200288634499802387117330052505693615
0964716943724997754073759586443897427456172764148625412832801640019356900337767271126113875736804626
2560003871576738389546309620240220160000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000 

 440   108446423039535872993215143801708248788897518439196551865815224471960229150134987551824227831
6824974396425374472199989051735746360755709387267704156375665474959707382975453596942334692582480660
4441231178941833620269043074841949435333742892131754367676600950973417767747377042144522193620421428
2140014849868367338680549949846121648321743392211378370176998833209921206655217464739831625543921041
2526487664089968857007109138790524864928123175632814919112439254273788773691427686404063230668247974
7213114796714097756841278925671075905040965622203570652239329167789023141169583945522024583639602764
8440861440543344125146667943578032458072195974008992176685068654594958348314899096787905903269227303
6724661022533504520746569434366728325919336695072199658573011889440262416239940442614450354771869281
4107138420936301106286615600332822535921841758178666499361272326153553003350453435945619719470682453
8502279255382972206034525278814354951808365156295137852239659582806470869382588169461649156300693104
2081669726890074865290348600834734599766478437790255612666824099267434364355484351860734906370740873
8153091824362150190119591404723642408437559324722797095860113927234179739555019658993005257297735756
2548306987001964447384676858917584692194740403103300719776568071910636020311087045555588606644758684
3252772445103269658421989147232174080000000000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000 

  Posted by Charlie on 2016-07-14 15:04:28
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