N(2)=1+1/2^2+2/3^2+5/4^2+4/5^2+2/6^2+6/7^2+....
kohmoto
zbi74583 at boat.zero.ad.jp
Wed Nov 8 06:33:16 CET 2006
Hi, Seqfans
I asked Mathar to calculate the following
number.
N(s)= Sum_{m=1 to infinity} (-1)Sigma(m)/m^s
See the end of this mail
I tried to find an identity like the following
Zeta(s)Zeta(s-1)=Sum_{m=1 to infinity} Sigma(m)/m^s
Zeta(s)/Zeta(s+1)=Sum_{m=1 to infinity} Phi(m)/m^s
But it is too difficult.
I transformed it a little as follows.
N(s)= Sum_{m=1 to infinity} (-1)Sigma(m)/m^s
= Product_{p_i} ( Sum_{k=0 to infinity}
(-1)Sigma(p_i^k)/p_i^(k*s) )
= Product_{p_i} ( Sum_{k=0 to infinity}
(Sigma(p_i^k)-2)/p_i^(k*s) )
= Product_{p_i} ( Sum_{k=0 to infinity}
Sigma(p_i^k)/p_i^(k*s) -2/(p_i^s-1) )
Some members of Seqfan might solve it easily.
Yasutsoshi
----- Original Message -----
From: "Richard Mathar" <mathar at strw.leidenuniv.nl>
To: <zbi74583 at boat.zero.ad.jp>
Cc: <mathar at mail.strw.leidenuniv.nl>
Sent: Sunday, November 05, 2006 10:35 PM
Subject: Re: N(2)=1+1/2^2+2/3^2+5/4^2+4/5^2+2/6^2+6/7^2+....
>
> These are 5 tables of partial sums of N(s) up to some maximum
> m of sum_{m=1...max(m)) (-1)Sigma(m)/m^s. The first number
> is s, the second the maximum m up to which the sum has been accumulated,
> and finally the floating point number the partial sum.
> The case s=1 seems not to be a converging series; the partial sums are
> almost
> linear to the upper limit of m. (If your formula with the zeta-function is
> correct, this is expected since zeta(1)=infinty.) I am including some
> values
> for small maximum m so you can check the results for the basic cases.
> N(2) seems to be a converging series. For N(3) you could already get some
> pretty accurate estimate of the series limit.
>
> zeta(2)=1.644934067
> zeta(3)=1.202056903
> zeta(4)=1.082323234
> zeta(3)*zeta(2)=1.977304350
> zeta(4)*zeta(3)=1.301014115
> zeta(5)*zeta(4)=1.122291001
>
>
> PARI:
>
> \\ computes (-1)sigma(n)
> A049060(n)={
> local(i,resul,rmax,p) ;
> if(n==1,
> return(1)
> ) ;
> i=factor(n) ;
> rmax=matsize(i)[1] ;
> resul=1 ;
> for(r=1,rmax,
> p=0 ;
> for(j=1,i[r,2],
> p += i[r,1]^j ;
> ) ;
> resul *= p-1 ;
> ) ;
> return(resul) ;
> }
>
>
> N(s,mmax)={
> local(resul) ;
> resul=0.0 ;
> for(m=1,mmax,
> resul += A049060(m)/m^s ;
> if(m<10 || (m % 10000 == 0),
> print(s," ",m," ",resul) ;
> ) ;
> ) ;
> }
>
> {
> mmax=1000000 ;
> for(s=1,5,
> N(s,mmax) ;
> ) ;
> }
>
> Tables:
>
> 1 1 1.000000000000000000000000000
> 1 2 1.500000000000000000000000000
> 1 3 2.166666666666666666666666667
> 1 4 3.416666666666666666666666667
> 1 5 4.216666666666666666666666667
> 1 6 4.550000000000000000000000000
> 1 7 5.407142857142857142857142857
> 1 8 7.032142857142857142857142857
> 1 9 8.254365079365079365079365079
> 1 10000 8956.254813409229652481598757
> 1 20000 17913.54053798274101959639246
> 1 30000 26870.58900461199889420226700
> 1 40000 35827.55225952432056619824099
> 1 50000 44784.92216728336777991954546
> 1 60000 53741.30998083683291788901077
> 1 70000 62698.82877172292127401143322
> 1 80000 71656.42458494024747176547617
> 1 90000 80613.31691563743683765060924
> 1 100000 89570.20047616274019702521482
> 1 110000 98527.44018335441754406085900
> 1 120000 107484.2058258699552949703883
> 1 130000 116441.3450587298928159003627
> 1 140000 125399.1600101618061663172293
> 1 150000 134355.0716257765731578804073
> 1 160000 143312.6869188725594888173896
> 1 170000 152270.1691945778107893068833
> 1 180000 161227.3673088893702787242209
> 1 190000 170184.2283671443801174189235
> 1 200000 179141.9177161676803505348327
> 1 210000 188098.1905736334290746346704
> 1 220000 197055.5778178213299226211954
> 1 230000 206012.3243951074382665848232
> 1 240000 214969.0180191522602672455303
> 1 250000 223927.0626654355275622417046
> 1 260000 232884.0479228396547382227555
> 1 270000 241841.6897312605543987962985
> 1 280000 250798.1260711861562596104630
> 1 290000 259755.4115589713808307871029
> 1 300000 268712.2473108133199765189322
> 1 310000 277669.3610844430796369732363
> 1 320000 286626.7360084187087594659096
> 1 330000 295583.0702328420388811375076
> 1 340000 304540.9324662583651406115180
> 1 350000 313497.9488508493337302810705
> 1 360000 322455.2848872162239393519675
> 1 370000 331411.9952274305516780284586
> 1 380000 340369.3878688847801453424847
> 1 390000 349326.5442385613025662494469
> 1 400000 358283.7198151948112652311070
> 1 410000 367240.8596635115166082534173
> 1 420000 376197.2486760902447184900822
> 1 430000 385154.6524560274677028589761
> 1 440000 394112.0480841471143112935114
> 1 450000 403069.2697966051366843904756
> 1 460000 412026.1487890321657369929892
> 1 470000 420983.4928713199267860102478
> 1 480000 429940.0597652682271439943634
> 1 490000 438897.5981659322519223492273
> 1 500000 447855.4516433798944040122164
> 1 510000 456811.4127981064830642426529
> 1 520000 465769.1531758862533175249594
> 1 530000 474726.4930671377953578153300
> 1 540000 483683.7925672078781534825684
> 1 550000 492640.2315981062235193108053
> 1 560000 501597.6949987133986923353009
> 1 570000 510554.3958474732897001847922
> 1 580000 519511.5431567859764988621906
> 1 590000 528468.5920184442509092919859
> 1 600000 537425.2057958757909274862160
> 1 610000 546383.3300255139505983850944
> 1 620000 555340.2697592667964924572269
> 1 630000 564297.7073054137624068690112
> 1 640000 573254.2920689474814450061694
> 1 650000 582211.4873730487914773223047
> 1 660000 591168.5211525597522567544916
> 1 670000 600125.8589826114248021714650
> 1 680000 609083.0330009002048275663287
> 1 690000 618039.4919349372313479054900
> 1 700000 626997.2222632460664089943429
> 1 710000 635954.0917690439691078847726
> 1 720000 644911.6290093784488180074886
> 1 730000 653868.6304875870104467000556
> 1 740000 662825.3447013751015479514900
> 1 750000 671782.5558801465303249818702
> 1 760000 680739.9011662731435592584669
> 1 770000 689696.9475041453715157412648
> 1 780000 698653.1437839886472918561286
> 1 790000 707611.0985532863373721850039
> 1 800000 716568.7987693866776749447598
> 1 810000 725525.6575122445531974385646
> 1 820000 734482.4569919820693082893669
> 1 830000 743439.4779916042359124217226
> 1 840000 752396.3611940500092646796766
> 1 850000 761353.5394438445571430835057
> 1 860000 770310.9434931792736520368474
> 1 870000 779267.1927223886953325647496
> 1 880000 788225.1436674517253585125689
>
>
> 2 1 1.000000000000000000000000000
> 2 2 1.250000000000000000000000000
> 2 3 1.472222222222222222222222222
> 2 4 1.784722222222222222222222222
> 2 5 1.944722222222222222222222222
> 2 6 2.000277777777777777777777778
> 2 7 2.122726757369614512471655329
> 2 8 2.325851757369614512471655329
> 2 9 2.461654226505416981607457798
> 2 10000 8.619813177975507784214344698
> 2 20000 9.240635095871089404115753095
> 2 30000 9.603791897573761358292380061
> 2 40000 9.861458278261452185262848858
> 2 50000 10.06133043757656995196303496
> 2 60000 10.22462154552329778519365923
> 2 70000 10.36270038005636494621123847
> 2 80000 10.48231016697477680498962023
> 2 90000 10.58780522013752853231672862
> 2 100000 10.68217402235127296288785820
> 2 110000 10.76754463607533705360724580
> 2 120000 10.84547789729425765394094918
> 2 130000 10.91717268365027978460835188
> 2 140000 10.98355652885066079792761960
> 2 150000 11.04534545539722125239381859
> 2 160000 11.10315629233238669062836862
> 2 170000 11.15746025373895516747888760
> 2 180000 11.20865775307751148407150182
> 2 190000 11.25708463818456648077093060
> 2 200000 11.30303121795283056763425981
> 2 210000 11.34672871948779384291766276
> 2 220000 11.38839827063844308711114745
> 2 230000 11.42821240662906506074836109
> 2 240000 11.46633165190016188934526342
> 2 250000 11.50290004647923375585461222
> 2 260000 11.53802980091084626273394586
> 2 270000 11.57183602344116902681335304
> 2 280000 11.60440829561909536077171934
> 2 290000 11.63584045378869260629085740
> 2 300000 11.66620539683007648663354504
> 2 310000 11.69557551635064846235471407
> 2 320000 11.72401391041322342493145640
> 2 330000 11.75157395832622563415629569
> 2 340000 11.77831576251751436463182945
> 2 350000 11.80427986574616427809478607
> 2 360000 11.82951337960016320803463309
> 2 370000 11.85405377158818097821428014
> 2 380000 11.87794149361683265940241605
> 2 390000 11.90120806565142413868457075
> 2 400000 11.92388559358277288937420440
> 2 410000 11.94600303970164868968234173
> 2 420000 11.96758569454234998141373716
> 2 430000 11.98866287480559328733313634
> 2 440000 12.00925544388189350449936925
> 2 450000 12.02938482345842327394291528
> 2 460000 12.04907101416111155199518539
> 2 470000 12.06833481184766752219695603
> 2 480000 12.08719139777266186606623586
> 2 490000 12.10566116650605692754670219
> 2 500000 12.12375840131307130932177405
> 2 510000 12.14149351071909408890611230
> 2 520000 12.15888769016783248485026059
> 2 530000 12.17594975401341942285000014
> 2 540000 12.19269280126406301090981599
> 2 550000 12.20912705098196862278557687
> 2 560000 12.22526702472305560991043337
> 2 570000 12.24111996896626519121471994
> 2 580000 12.25669798166764128539680162
> 2 590000 12.27200952384435815319104573
> 2 600000 12.28706299338740013449483108
> 2 610000 12.30187012252190226181814868
> 2 620000 12.31643453756242668558457904
> 2 630000 12.33076670711890682146429120
> 2 640000 12.34487182648867321005497632
> 2 650000 12.35875920337989470739102627
> 2 660000 12.37243430644503889140869087
> 2 670000 12.38590421689421153982279985
> 2 680000 12.39917431914306915108546756
> 2 690000 12.41224965443445935379058168
> 2 700000 12.42513867918653815467126754
> 2 710000 12.43784365088579118428209464
> 2 720000 12.45037185509338005878377820
> 2 730000 12.46272650898502725121177200
> 2 740000 12.47491268376206272216237202
> 2 750000 12.48693594951832440956683550
> 2 760000 12.49880013638169511883229569
> 2 770000 12.51050884124405914256853750
> 2 780000 12.52206537108093533871333277
> 2 790000 12.53347692259745252540675575
> 2 800000 12.54474459716977128685280547
> 2 810000 12.55587125001645305770022096
> 2 820000 12.56686130746829341595469366
> 2 830000 12.57771842011223665163037795
> 2 840000 12.58844534265072464040923243
> 2 850000 12.59904566706465055360427300
> 2 860000 12.60952226922408394518254911
> 2 870000 12.61987642201166975414741555
> 2 880000 12.63011418303496833362065684
> 2 890000 12.64023571583693921823484395
> 2 900000 12.65024408926657285403820450
> 2 910000 12.66014049405210257196085418
> 2 920000 12.66993013960070545251999449
> 2 930000 12.67961329658082585267888159
> 2 940000 12.68919341076487592672709130
> 2 950000 12.69867217785123447166660908
> 2 960000 12.70805040456023104531710849
> 2 970000 12.71733330696500792660758365
> 2 980000 12.72652037909829933006161382
> 2 990000 12.73561385879130711822105048
> 2 1000000 12.74461639944508312563225494
>
>
> 3 1 1.000000000000000000000000000
> 3 2 1.125000000000000000000000000
> 3 3 1.199074074074074074074074074
> 3 4 1.277199074074074074074074074
> 3 5 1.309199074074074074074074074
> 3 6 1.318458333333333333333333333
> 3 7 1.335951044703595724003887269
> 3 8 1.361341669703595724003887269
> 3 9 1.376430832940907109463420877
> 3 10000 1.463913982110741753040591678
> 3 20000 1.463958761182127253891639226
> 3 30000 1.463973687899719174955107484
> 3 40000 1.463981151485566123839035784
> 3 50000 1.463985629911768534082474807
> 3 60000 1.463988615257603046255509048
> 3 70000 1.463990747941060935932260523
> 3 80000 1.463992347452072574407883095
> 3 90000 1.463993591418911296987275373
> 3 100000 1.463994586598910692322299337
> 3 110000 1.463995400874372718599240224
> 3 120000 1.463996079403452056486658683
> 3 130000 1.463996653569731083112186861
> 3 140000 1.463997145746936259101012298
> 3 150000 1.463997572212239449568643565
> 3 160000 1.463997945442508018944894819
> 3 170000 1.463998274756427172013405468
> 3 180000 1.463998567470471281896562070
> 3 190000 1.463998829362945706567178177
> 3 200000 1.463999065087923587578410681
> 3 210000 1.463999278329572278322382185
> 3 220000 1.463999472210290336272529678
> 3 230000 1.463999649219477985324795694
> 3 240000 1.463999811477588227637144335
> 3 250000 1.463999960777271571969049099
> 3 260000 1.464000098575628251036076097
> 3 270000 1.464000226175768714632044135
> 3 280000 1.464000344645861174695942201
> 3 290000 1.464000454956284414358238477
> 3 300000 1.464000557907605374141443674
> 3 310000 1.464000654220015163939180059
> 3 320000 1.464000744515464470055773720
> 3 330000 1.464000829328753859822237621
> 3 340000 1.464000909166687500211857215
> 3 350000 1.464000984435262908416401907
> 3 360000 1.464001055524739843653406744
> 3 370000 1.464001122766895437258623701
> 3 380000 1.464001186474841361410807209
> 3 390000 1.464001246914091200041356493
> 3 400000 1.464001304331492624240843891
> 3 410000 1.464001358947841911631088786
> 3 420000 1.464001410959152183436079651
> 3 430000 1.464001460557008749462202957
> 3 440000 1.464001507900298795165105625
> 3 450000 1.464001553138542176224706874
> 3 460000 1.464001596408268761316169011
> 3 470000 1.464001637838876141306278665
> 3 480000 1.464001677539798346550656570
> 3 490000 1.464001715624418180233792011
> 3 500000 1.464001752186865804286414230
> 3 510000 1.464001787308096983826068464
> 3 520000 1.464001821085252219783666269
> 3 530000 1.464001853586288170141300728
> 3 540000 1.464001884883421221311137792
> 3 550000 1.464001915039618326560450277
> 3 560000 1.464001944122159842425557477
> 3 570000 1.464001972181866862157721242
> 3 580000 1.464001999275380923272745020
> 3 590000 1.464002025450188768071703730
> 3 600000 1.464002050751299694154935270
> 3 610000 1.464002075226966770079630464
> 3 620000 1.464002098909928297454328876
> 3 630000 1.464002121842320025653578842
> 3 640000 1.464002144055977272720855659
> 3 650000 1.464002165587616796774276693
> 3 660000 1.464002186466412269783936185
> 3 670000 1.464002206722643544544226821
> 3 680000 1.464002226382732127695424983
> 3 690000 1.464002245471462412103956612
> 3 700000 1.464002264017435494080639785
> 3 710000 1.464002282039246813434225341
> 3 720000 1.464002299561748289079351576
> 3 730000 1.464002316603153605988980695
> 3 740000 1.464002333183468992396940641
> 3 750000 1.464002349322542550155865090
> 3 760000 1.464002365037130225625255935
> 3 770000 1.464002380343037616331619950
> 3 780000 1.464002395255086253184010138
> 3 790000 1.464002409792474848650673824
> 3 800000 1.464002423965997236326475471
> 3 810000 1.464002437788253358795504488
> 3 820000 1.464002451273302166423360831
> 3 830000 1.464002464433742258170070393
> 3 840000 1.464002477280648906020788669
> 3 850000 1.464002489825692224210435982
> 3 860000 1.464002502079291985535094261
> 3 870000 1.464002514049668308408128899
> 3 880000 1.464002525750211478039722139
> 3 890000 1.464002537187197706443946991
> 3 900000 1.464002548369947911638829284
> 3 910000 1.464002559305408714470469907
> 3 920000 1.464002570004676399632165939
> 3 930000 1.464002580473145840547517414
> 3 940000 1.464002590719441673840433620
> 3 950000 1.464002600750056430793286939
> 3 960000 1.464002610570359301053681776
> 3 970000 1.464002620190111512591642127
> 3 980000 1.464002629612902400536905838
> 3 990000 1.464002638845007329954067381
> 3 1000000 1.464002647892926094713436024
>
>
> 4 1 1.000000000000000000000000000
> 4 2 1.062500000000000000000000000
> 4 3 1.087191358024691358024691358
> 4 4 1.106722608024691358024691358
> 4 5 1.113122608024691358024691358
> 4 6 1.114665817901234567901234568
> 4 7 1.117164776668414909425599416
> 4 8 1.120338604793414909425599416
> 4 9 1.122015178486449507809992039
> 4 10000 1.126342859836933119635341727
> 4 20000 1.126342863195068461987333491
> 4 30000 1.126342863816977724856173635
> 4 40000 1.126342864034657367890755384
> 4 50000 1.126342864135419045299551969
> 4 60000 1.126342864190149270391012376
> 4 70000 1.126342864223154637804140480
> 4 80000 1.126342864244576264194082203
> 4 90000 1.126342864259261709833237965
> 4 100000 1.126342864269766231843710036
> 4 110000 1.126342864277538770311620766
> 4 120000 1.126342864283450137689488953
> 4 130000 1.126342864288050791700191891
> 4 140000 1.126342864291701518257416350
> 4 150000 1.126342864294646135946293287
> 4 160000 1.126342864297056569571605552
> 4 170000 1.126342864299054229967212718
> 4 180000 1.126342864300728234359584700
> 4 190000 1.126342864302144893188134103
> 4 200000 1.126342864303354525085913547
> 4 210000 1.126342864304395340180474300
> 4 220000 1.126342864305297594007409955
> 4 230000 1.126342864306084686590084820
> 4 240000 1.126342864306775457553279160
> 4 250000 1.126342864307385095784161975
> 4 260000 1.126342864307925686556878209
> 4 270000 1.126342864308407364997509003
> 4 280000 1.126342864308838305443671084
> 4 290000 1.126342864309225477016399704
> 4 300000 1.126342864309574563445429650
> 4 310000 1.126342864309890425673710622
> 4 320000 1.126342864310177149073405791
> 4 330000 1.126342864310438174074903581
> 4 340000 1.126342864310676548757732228
> 4 350000 1.126342864310894763694630232
> 4 360000 1.126342864311095054783294446
> 4 370000 1.126342864311279313873956099
> 4 380000 1.126342864311449231412772564
> 4 390000 1.126342864311606242436985681
> 4 400000 1.126342864311751625747966668
> 4 410000 1.126342864311886501047539562
> 4 420000 1.126342864312011847410167188
> 4 430000 1.126342864312128564203286214
> 4 440000 1.126342864312237413459871362
> 4 450000 1.126342864312339084988654298
> 4 460000 1.126342864312434194531858928
> 4 470000 1.126342864312523302682800842
> 4 480000 1.126342864312606892652019146
> 4 490000 1.126342864312685425831403550
> 4 500000 1.126342864312759296677644308
> 4 510000 1.126342864312828850304390296
> 4 520000 1.126342864312894443054768726
> 4 530000 1.126342864312956355217879326
> 4 540000 1.126342864313014859446213372
> 4 550000 1.126342864313070196425470463
> 4 560000 1.126342864313122601535952824
> 4 570000 1.126342864313172268506265819
> 4 580000 1.126342864313219391141266622
> 4 590000 1.126342864313264137597311253
> 4 600000 1.126342864313306663426890322
> 4 610000 1.126342864313347121770685419
> 4 620000 1.126342864313385633102777798
> 4 630000 1.126342864313422327185152818
> 4 640000 1.126342864313457311416964776
> 4 650000 1.126342864313490695748042037
> 4 660000 1.126342864313522573574899694
> 4 670000 1.126342864313553035740126664
> 4 680000 1.126342864313582163334291352
> 4 690000 1.126342864313610031536993753
> 4 700000 1.126342864313636717733889822
> 4 710000 1.126342864313662281830870319
> 4 720000 1.126342864313686789977325667
> 4 730000 1.126342864313710296430980716
> 4 740000 1.126342864313732855692110296
> 4 750000 1.126342864313754519823275656
> 4 760000 1.126342864313775334724375007
> 4 770000 1.126342864313795343268423855
> 4 780000 1.126342864313814585400999315
> 4 790000 1.126342864313833105102330919
> 4 800000 1.126342864313850934103761246
> 4 810000 1.126342864313868105235437633
> 4 820000 1.126342864313884651902605718
> 4 830000 1.126342864313900604514476466
> 4 840000 1.126342864313915990566003172
> 4 850000 1.126342864313930837276585851
> 4 860000 1.126342864313945169444268968
> 4 870000 1.126342864313959008481394737
> 4 880000 1.126342864313972380956143569
> 4 890000 1.126342864313985304497313295
> 4 900000 1.126342864313997799554982470
> 4 910000 1.126342864314009883288627525
> 4 920000 1.126342864314021576813991216
> 4 930000 1.126342864314032894395637362
> 4 940000 1.126342864314043853302500574
> 4 950000 1.126342864314054467992200910
> 4 960000 1.126342864314064751304010854
> 4 970000 1.126342864314074720218563997
> 4 980000 1.126342864314084384860927016
> 4 990000 1.126342864314093757784864329
> 4 1000000 1.126342864314102851387025112
>
>
> 5 1 1.000000000000000000000000000
> 5 2 1.031250000000000000000000000
> 5 3 1.039480452674897119341563786
> 5 4 1.044363265174897119341563786
> 5 5 1.045643265174897119341563786
> 5 6 1.045900466820987654320987654
> 5 7 1.046257460930584845967325490
> 5 8 1.046654189446209845967325490
> 5 9 1.046840475412102579121146892
> 5 10000 1.047127646962981639236350714
> 5 20000 1.047127646963242803683634380
> 5 30000 1.047127646963269060444667980
> 5 40000 1.047127646963275452376929668
> 5 50000 1.047127646963277728778610486
> 5 60000 1.047127646963278734909173763
> 5 70000 1.047127646963279246707166974
> 5 80000 1.047127646963279534023699805
> 5 90000 1.047127646963279707590251386
> 5 100000 1.047127646963279818572046343
> 5 110000 1.047127646963279892819669335
> 5 120000 1.047127646963279944352143863
> 5 130000 1.047127646963279981235720216
> 5 140000 1.047127646963280008327383488
> 5 150000 1.047127646963280028667159600
> 5 160000 1.047127646963280044239866946
> 5 170000 1.047127646963280056361640181
> 5 180000 1.047127646963280065937720739
> 5 190000 1.047127646963280073602739981
> 5 200000 1.047127646963280079811373591
> 5 210000 1.047127646963280084892514359
> 5 220000 1.047127646963280089092048700
> 5 230000 1.047127646963280092592526331
> 5 240000 1.047127646963280095533744603
> 5 250000 1.047127646963280098023437624
> 5 260000 1.047127646963280100144477685
> 5 270000 1.047127646963280101962983953
> 5 280000 1.047127646963280103530722491
> 5 290000 1.047127646963280104889770905
> 5 300000 1.047127646963280106073563423
> 5 310000 1.047127646963280107109545028
> 5 320000 1.047127646963280108020080532
> 5 330000 1.047127646963280108823485592
> 5 340000 1.047127646963280109535261396
> 5 350000 1.047127646963280110167943658
> 5 360000 1.047127646963280110732291221
> 5 370000 1.047127646963280111237235413
> 5 380000 1.047127646963280111690454876
> 5 390000 1.047127646963280112098366088
> 5 400000 1.047127646963280112466502499
> 5 410000 1.047127646963280112799594529
> 5 420000 1.047127646963280113101691720
> 5 430000 1.047127646963280113376369686
> 5 440000 1.047127646963280113626641318
> 5 450000 1.047127646963280113855154497
> 5 460000 1.047127646963280114064219587
> 5 470000 1.047127646963280114255879066
> 5 480000 1.047127646963280114431883567
> 5 490000 1.047127646963280114593830274
> 5 500000 1.047127646963280114743084164
> 5 510000 1.047127646963280114880831757
> 5 520000 1.047127646963280115008212055
> 5 530000 1.047127646963280115126153891
> 5 540000 1.047127646963280115235519959
> 5 550000 1.047127646963280115337066821
> 5 560000 1.047127646963280115431500449
> 5 570000 1.047127646963280115519415563
> 5 580000 1.047127646963280115601376090
> 5 590000 1.047127646963280115677873082
> 5 600000 1.047127646963280115749351712
> 5 610000 1.047127646963280115816230987
> 5 620000 1.047127646963280115878856405
> 5 630000 1.047127646963280115937571799
> 5 640000 1.047127646963280115992669514
> 5 650000 1.047127646963280116044432219
> 5 660000 1.047127646963280116093104355
> 5 670000 1.047127646963280116138915493
> 5 680000 1.047127646963280116182070550
> 5 690000 1.047127646963280116222756887
> 5 700000 1.047127646963280116261156889
> 5 710000 1.047127646963280116297420392
> 5 720000 1.047127646963280116331699689
> 5 730000 1.047127646963280116364124370
> 5 740000 1.047127646963280116394819088
> 5 750000 1.047127646963280116423900164
> 5 760000 1.047127646963280116451471135
> 5 770000 1.047127646963280116477627542
> 5 780000 1.047127646963280116502457450
> 5 790000 1.047127646963280116526050682
> 5 800000 1.047127646963280116548478239
> 5 810000 1.047127646963280116569809891
> 5 820000 1.047127646963280116590113535
> 5 830000 1.047127646963280116609450953
> 5 840000 1.047127646963280116627878223
> 5 850000 1.047127646963280116645449098
> 5 860000 1.047127646963280116662212610
> 5 870000 1.047127646963280116678212198
> 5 880000 1.047127646963280116693495678
> 5 890000 1.047127646963280116708099149
> 5 900000 1.047127646963280116722060660
> 5 910000 1.047127646963280116735413376
> 5 920000 1.047127646963280116748193681
> 5 930000 1.047127646963280116760429366
> 5 940000 1.047127646963280116772150557
> 5 950000 1.047127646963280116783383436
> 5 960000 1.047127646963280116794151686
> 5 970000 1.047127646963280116804482528
> 5 980000 1.047127646963280116814395317
> 5 990000 1.047127646963280116823911289
> 5 1000000 1.047127646963280116833050882
>
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