3176:
1099:
3171:{\displaystyle {\begin{aligned}\operatorname {Ta} (7)\leq &\ 24885189317885898975235988544\\&=2648660966^{3}+1847282122^{3}\\&=2685635652^{3}+1766742096^{3}\\&=2736414008^{3}+1638024868^{3}\\&=2894406187^{3}+860447381^{3}\\&=2915734948^{3}+459531128^{3}\\&=2918375103^{3}+309481473^{3}\\&=2919526806^{3}+58798362^{3}\\\operatorname {Ta} (8)\leq &\ 50974398750539071400590819921724352\\&=299512063576^{3}+288873662876^{3}\\&=336379942682^{3}+234604829494^{3}\\&=341075727804^{3}+224376246192^{3}\\&=347524579016^{3}+208029158236^{3}\\&=367589585749^{3}+109276817387^{3}\\&=370298338396^{3}+58360453256^{3}\\&=370633638081^{3}+39304147071^{3}\\&=370779904362^{3}+7467391974^{3}\\\operatorname {Ta} (9)\leq &\ 136897813798023990395783317207361432493888\\&=41632176837064^{3}+40153439139764^{3}\\&=46756812032798^{3}+32610071299666^{3}\\&=47409526164756^{3}+31188298220688^{3}\\&=48305916483224^{3}+28916052994804^{3}\\&=51094952419111^{3}+15189477616793^{3}\\&=51471469037044^{3}+8112103002584^{3}\\&=51518075693259^{3}+5463276442869^{3}\\&=51530042142656^{3}+4076877805588^{3}\\&=51538406706318^{3}+1037967484386^{3}\\\operatorname {Ta} (10)\leq &\ 7335345315241855602572782233444632535674275447104\\&=15695330667573128^{3}+15137846555691028^{3}\\&=17627318136364846^{3}+12293996879974082^{3}\\&=17873391364113012^{3}+11757988429199376^{3}\\&=18211330514175448^{3}+10901351979041108^{3}\\&=19262797062004847^{3}+5726433061530961^{3}\\&=19404743826965588^{3}+3058262831974168^{3}\\&=19422314536358643^{3}+2059655218961613^{3}\\&=19426825887781312^{3}+1536982932706676^{3}\\&=19429379778270560^{3}+904069333568884^{3}\\&=19429979328281886^{3}+391313741613522^{3}\\\operatorname {Ta} (11)\leq &\ 2818537360434849382734382145310807703728251895897826621632\\&=11410505395325664056^{3}+11005214445987377356^{3}\\&=12815060285137243042^{3}+8937735731741157614^{3}\\&=12993955521710159724^{3}+8548057588027946352^{3}\\&=13239637283805550696^{3}+7925282888762885516^{3}\\&=13600192974314732786^{3}+6716379921779399326^{3}\\&=14004053464077523769^{3}+4163116835733008647^{3}\\&=14107248762203982476^{3}+2223357078845220136^{3}\\&=14120022667932733461^{3}+1497369344185092651^{3}\\&=14123302420417013824^{3}+1117386592077753452^{3}\\&=14125159098802697120^{3}+657258405504578668^{3}\\&=14125594971660931122^{3}+284485090153030494^{3}\\\operatorname {Ta} (12)\leq &\ 73914858746493893996583617733225161086864012865017882136931801625152\\&=33900611529512547910376^{3}+32696492119028498124676^{3}\\&=38073544107142749077782^{3}+26554012859002979271194^{3}\\&=38605041855000884540004^{3}+25396279094031028611792^{3}\\&=39334962370186291117816^{3}+23546015462514532868036^{3}\\&=40406173326689071107206^{3}+19954364747606595397546^{3}\\&=41606042841774323117699^{3}+12368620118962768690237^{3}\\&=41912636072508031936196^{3}+6605593881249149024056^{3}\\&=41950587346428151112631^{3}+4448684321573910266121^{3}\\&=41960331491058948071104^{3}+3319755565063005505892^{3}\\&=41965847682542813143520^{3}+1952714722754103222628^{3}\\&=41965889731136229476526^{3}+1933097542618122241026^{3}\\&=41967142660804626363462^{3}+845205202844653597674^{3}\end{aligned}}}
1085:
196:
1080:{\displaystyle {\begin{aligned}\operatorname {Ta} (1)=&\ 2\\&=1^{3}+1^{3}\\\operatorname {Ta} (2)=&\ 1729\\&=1^{3}+12^{3}\\&=9^{3}+10^{3}\\\operatorname {Ta} (3)=&\ 87539319\\&=167^{3}+436^{3}\\&=228^{3}+423^{3}\\&=255^{3}+414^{3}\\\operatorname {Ta} (4)=&\ 6963472309248\\&=2421^{3}+19083^{3}\\&=5436^{3}+18948^{3}\\&=10200^{3}+18072^{3}\\&=13322^{3}+16630^{3}\\\operatorname {Ta} (5)=&\ 48988659276962496\\&=38787^{3}+365757^{3}\\&=107839^{3}+362753^{3}\\&=205292^{3}+342952^{3}\\&=221424^{3}+336588^{3}\\&=231518^{3}+331954^{3}\\\operatorname {Ta} (6)=&\ 24153319581254312065344\\&=582162^{3}+28906206^{3}\\&=3064173^{3}+28894803^{3}\\&=8519281^{3}+28657487^{3}\\&=16218068^{3}+27093208^{3}\\&=17492496^{3}+26590452^{3}\\&=18289922^{3}+26224366^{3}\end{aligned}}}
1104:
201:
3524:
163:
obtained Ta(3) in 1957. E. Rosenstiel, J. A. Dardis and C. R. Rosenstiel found Ta(4) in 1989. J. A. Dardis found Ta(5) in 1994 and it was confirmed by David W. Wilson in 1999. Ta(6) was announced by Uwe
Hollerbach on the NMBRTHRY mailing list on March 9, 2008, following a 2003 paper by Calude et al.
27:
3363:
3372:
116:, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
3244:
3377:
3249:
3519:{\displaystyle {\begin{aligned}1801049058342701083&=92227^{3}+1216500^{3}\\&=136635^{3}+1216102^{3}\\&=341995^{3}+1207602^{3}\\&=600259^{3}+1165884^{3}\end{aligned}}}
179:
has been introduced to allow for alternative, less restrictive definitions of this nature. In a sense, the specification of two summands and powers of three is also restrictive; a
3969:
148:, and their proof is easily converted into a program to generate such numbers. However, the proof makes no claims at all about whether the thus-generated numbers are
171:
to positive numbers is necessary, because allowing negative numbers allows for more (and smaller) instances of numbers that can be expressed as sums of cubes in
3533:
3780:
3585:
3367:
The smallest cubefree taxicab number with four representations was discovered by Stuart
Gascoigne and independently by Duncan Moore in 2003:
3682:
129:, who published his observation in 1657. 1729 was made famous as the first taxicab number in the early 20th century by a story involving
3558:
164:
that gave a 99% probability that the number was actually Ta(6). Upper bounds for Ta(7) to Ta(12) were found by
Christian Boyer in 2006.
3757:
3358:{\displaystyle {\begin{aligned}15170835645&=517^{3}+2468^{3}\\&=709^{3}+2456^{3}\\&=1733^{3}+2152^{3}\end{aligned}}}
3768:
3999:
3605: – List of mathematical contexts in which exponentiated terms are summed, a list of related conjectures and theorems
4055:
126:
3702:
3579:
3564:
180:
160:
3235:
are cubefree taxicab numbers. The smallest cubefree taxicab number with three representations was discovered by
3769:
NMBRTHRY Archives – March 2008 (#10) "The sixth taxicab number is 24153319581254312065344" by Uwe
Hollerbach
4050:
3900:
3590:
3570:
3552:
3698:
3596:
130:
101:
30:
3722:
3679:
3189:, which means that it is not divisible by any cube other than 1. When a cubefree taxicab number
26:
37:) was bedridden when he developed the idea of taxicab numbers, according to an anecdote from
3890:. (Wilson was unaware of J. A. Dardis' prior discovery of Ta(5) in 1994 when he wrote this.)
3714:
3216:
3868:
3641:
3593: – Four integers where the sum of the squares of three equals the square of the fourth
3865:
3686:
125:
The pairs of summands of the Hardy–Ramanujan number Ta(2) = 1729 were first mentioned by
4010:
3664:
3887:
3602:
176:
133:
in claiming it to be the smallest for his particular example of two summands. In 1938,
69:
20:
3793:"'New Upper Bounds for Taxicab and Cabtaxi Numbers" Christian Boyer, France, 2006–2008
3567: – Smallest number expressable as the sum of j numbers to the kth power in n ways
16:
Smallest integer expressable as a sum of two positive integer cubes in n distinct ways
4044:
3546:
113:
94:
77:
3826:
The four least solutions in distinct positive integers of the
Diophantine equations
3623:
138:
4033:
4029:
4025:
4006:
3660:
134:
97:
46:
38:
3872:
3236:
159:
The taxicab numbers subsequent to 1729 were found with the help of computers.
3779:
C. S. Calude, E. Calude and M. J. Dinneen: What is the value of
Taxicab(6)?,
65:), is defined as the smallest integer that can be expressed as a sum of two
3792:
3186:
168:
3726:
3185:
A more restrictive taxicab problem requires that the taxicab number be
142:
3739:
Numbers Count column, Personal
Computer World, page 234, November 1989
183:
allows for these values to be other than two and three, respectively.
109:
80:= Ta(2) = 1 + 12 = 9 + 10, also known as the Hardy-Ramanujan number.
3810:, 3rd ed., Oxford University Press, London & NY, 1954, Thm. 412.
3718:
2766:
73914858746493893996583617733225161086864012865017882136931801625152
4000:
A 2002 post to the Number Theory mailing list by
Randall L. Rathbun
3748:
Numbers Count column of
Personal Computer World, page 610, Feb 1995
3758:"The Fifth Taxicab Number is 48988659276962496" by David W. Wilson
25:
3555: – Polynomial equation whose integer solutions are sought
3582: – Diophantine equation attributed to Jacobi and Madden
3528:
108:
I remember once going to see him when he was lying ill at
3680:
Quotations by G. H. Hardy, MacTutor
History of Mathematics
2373:
2818537360434849382734382145310807703728251895897826621632
1094:
For the following taxicab numbers upper bounds are known:
4019:
152:
and so it cannot be used to find the actual value of Ta(
3575:
Pages displaying short descriptions of redirect targets
3239:(unpublished) in 1981 while he was a graduate student:
3903:
3375:
3247:
1102:
199:
19:
For number plates assigned to vehicles for hire, see
191:So far, the following 6 taxicab numbers are known:
3963:
3824:E. Rosenstiel, J. A. Dardis and C. R. Rosenstiel,
3518:
3357:
3170:
1079:
2013:7335345315241855602572782233444632535674275447104
76:distinct ways. The most famous taxicab number is
141:proved that such numbers exist for all positive
4012:1729: Taxi Cab Number or Hardy-Ramanujan Number
3666:1729: Taxi Cab Number or Hardy-Ramanujan Number
106:
3880:The Fifth Taxicab Number is 48988659276962496
3561: – Disproved conjecture in number theory
8:
3981:C. S. Calude, E. Calude and M. J. Dinneen:
1686:136897813798023990395783317207361432493888
3902:
3506:
3493:
3473:
3460:
3440:
3427:
3407:
3394:
3376:
3374:
3345:
3332:
3312:
3299:
3279:
3266:
3248:
3246:
3158:
3145:
3125:
3112:
3092:
3079:
3059:
3046:
3026:
3013:
2993:
2980:
2960:
2947:
2927:
2914:
2894:
2881:
2861:
2848:
2828:
2815:
2795:
2782:
2732:
2719:
2699:
2686:
2666:
2653:
2633:
2620:
2600:
2587:
2567:
2554:
2534:
2521:
2501:
2488:
2468:
2455:
2435:
2422:
2402:
2389:
2339:
2326:
2306:
2293:
2273:
2260:
2240:
2227:
2207:
2194:
2174:
2161:
2141:
2128:
2108:
2095:
2075:
2062:
2042:
2029:
1979:
1966:
1946:
1933:
1913:
1900:
1880:
1867:
1847:
1834:
1814:
1801:
1781:
1768:
1748:
1735:
1715:
1702:
1652:
1639:
1619:
1606:
1586:
1573:
1553:
1540:
1520:
1507:
1487:
1474:
1454:
1441:
1421:
1408:
1358:
1345:
1325:
1312:
1292:
1279:
1259:
1246:
1226:
1213:
1193:
1180:
1160:
1147:
1103:
1101:
1067:
1054:
1034:
1021:
1001:
988:
968:
955:
935:
922:
902:
889:
839:
826:
806:
793:
773:
760:
740:
727:
707:
694:
644:
631:
611:
598:
578:
565:
545:
532:
482:
469:
449:
436:
416:
403:
353:
340:
320:
307:
257:
244:
200:
198:
3808:An Introduction to the Theory of Numbers
83:The name is derived from a conversation
3815:Some Solutions of Diophantine Equations
3615:
3987:Journal of Universal Computer Science
3781:Journal of Universal Computer Science
7:
3964:{\displaystyle p(a)+q(b)=r(c)+s(d)}
1392:50974398750539071400590819921724352
3989:, Vol. 9 (2003), p. 1196–1203
14:
175:distinct ways. The concept of a
4020:Taxicab and other maths at Euler
3983:What is the value of Taxicab(6)?
3703:"Taxicabs and sums of two cubes"
3599: – Problem in number theory
3559:Euler's sum of powers conjecture
1090:Upper bounds for taxicab numbers
3573: – Mathematical conjecture
112:. I had ridden in taxi-cab No.
3958:
3952:
3943:
3937:
3928:
3922:
3913:
3907:
3806:G. H. Hardy and E. M. Wright,
3783:, Vol. 9 (2003), pp. 1196–1203
3549: – Hardy-Ramanujan number
2754:
2748:
2361:
2355:
2001:
1995:
1674:
1668:
1380:
1374:
1119:
1113:
861:
855:
666:
660:
504:
498:
375:
369:
279:
273:
216:
210:
1:
4034:"Taxicab Numbers in Futurama"
4005:Grime, James; Bowley, Roger.
3659:Grime, James; Bowley, Roger.
1131:24885189317885898975235988544
3884:Journal of Integer Sequences
3586:Prouhet–Tarry–Escott problem
3219:. Among the taxicab numbers
4072:
3976:Mathematics of Computation
3565:Generalized taxicab number
181:generalized taxicab number
18:
3895:Enumerating solutions to
127:Bernard Frénicle de Bessy
3978:70, 233 (2000), 389–394.
3642:"Hardy-Ramanujan Number"
3181:Cubefree taxicab numbers
3862:Bull. Inst. Math. Appl.
3143:41967142660804626363462
3110:41965889731136229476526
3077:41965847682542813143520
3044:41960331491058948071104
3011:41950587346428151112631
2978:41912636072508031936196
2958:12368620118962768690237
2945:41606042841774323117699
2925:19954364747606595397546
2912:40406173326689071107206
2892:23546015462514532868036
2879:39334962370186291117816
2859:25396279094031028611792
2846:38605041855000884540004
2826:26554012859002979271194
2813:38073544107142749077782
2793:32696492119028498124676
2780:33900611529512547910376
873:24153319581254312065344
167:The restriction of the
57:, typically denoted Ta(
3965:
3819:Proc. Camb. Phil. Soc.
3580:Jacobi–Madden equation
3520:
3359:
3172:
3123:1933097542618122241026
3090:1952714722754103222628
3057:3319755565063005505892
3024:4448684321573910266121
2991:6605593881249149024056
1081:
121:History and definition
118:
42:
3966:
3591:Pythagorean quadruple
3521:
3360:
3173:
3156:845205202844653597674
1082:
187:Known taxicab numbers
150:the smallest possible
29:
3901:
3864:, 27(1991) 155–157;
3699:Silverman, Joseph H.
3553:Diophantine equation
3373:
3245:
2717:14125594971660931122
2684:14125159098802697120
2651:14123302420417013824
2618:14120022667932733461
2585:14107248762203982476
2552:14004053464077523769
2519:13600192974314732786
2486:13239637283805550696
2453:12993955521710159724
2420:12815060285137243042
2400:11005214445987377356
2387:11410505395325664056
1100:
197:
104:. As told by Hardy:
4056:Srinivasa Ramanujan
3707:Amer. Math. Monthly
3597:Sums of three cubes
3381:1801049058342701083
3227:listed above, only
2664:1117386592077753452
2631:1497369344185092651
2598:2223357078845220136
2565:4163116835733008647
2532:6716379921779399326
2499:7925282888762885516
2466:8548057588027946352
2433:8937735731741157614
131:Srinivasa Ramanujan
102:Srinivasa Ramanujan
31:Srinivasa Ramanujan
3961:
3821:53, 778–780, 1957.
3685:2012-07-16 at the
3516:
3514:
3355:
3353:
3168:
3166:
2730:284485090153030494
2697:657258405504578668
1077:
1075:
43:
3893:D. J. Bernstein,
3886:, Vol. 2 (1999),
3878:David W. Wilson,
3646:Wolfram Mathworld
3628:Wolfram Mathworld
3571:Beal's conjecture
2764:
2371:
2324:19429979328281886
2291:19429379778270560
2258:19426825887781312
2225:19422314536358643
2192:19404743826965588
2159:19262797062004847
2139:10901351979041108
2126:18211330514175448
2106:11757988429199376
2093:17873391364113012
2073:12293996879974082
2060:17627318136364846
2040:15137846555691028
2027:15695330667573128
2011:
1684:
1390:
1129:
871:
678:48988659276962496
676:
514:
385:
289:
226:
4063:
4037:
4016:
3972:
3970:
3968:
3967:
3962:
3795:
3790:
3784:
3777:
3771:
3766:
3760:
3755:
3749:
3746:
3740:
3737:
3731:
3730:
3695:
3689:
3677:
3671:
3670:
3656:
3650:
3649:
3638:
3632:
3631:
3624:"Taxicab Number"
3620:
3576:
3531:
3525:
3523:
3522:
3517:
3515:
3511:
3510:
3498:
3497:
3482:
3478:
3477:
3465:
3464:
3449:
3445:
3444:
3432:
3431:
3416:
3412:
3411:
3399:
3398:
3364:
3362:
3361:
3356:
3354:
3350:
3349:
3337:
3336:
3321:
3317:
3316:
3304:
3303:
3288:
3284:
3283:
3271:
3270:
3234:
3230:
3226:
3217:relatively prime
3214:
3210:
3206:
3192:
3177:
3175:
3174:
3169:
3167:
3163:
3162:
3150:
3149:
3134:
3130:
3129:
3117:
3116:
3101:
3097:
3096:
3084:
3083:
3068:
3064:
3063:
3051:
3050:
3035:
3031:
3030:
3018:
3017:
3002:
2998:
2997:
2985:
2984:
2969:
2965:
2964:
2952:
2951:
2936:
2932:
2931:
2919:
2918:
2903:
2899:
2898:
2886:
2885:
2870:
2866:
2865:
2853:
2852:
2837:
2833:
2832:
2820:
2819:
2804:
2800:
2799:
2787:
2786:
2771:
2762:
2737:
2736:
2724:
2723:
2708:
2704:
2703:
2691:
2690:
2675:
2671:
2670:
2658:
2657:
2642:
2638:
2637:
2625:
2624:
2609:
2605:
2604:
2592:
2591:
2576:
2572:
2571:
2559:
2558:
2543:
2539:
2538:
2526:
2525:
2510:
2506:
2505:
2493:
2492:
2477:
2473:
2472:
2460:
2459:
2444:
2440:
2439:
2427:
2426:
2411:
2407:
2406:
2394:
2393:
2378:
2369:
2344:
2343:
2331:
2330:
2315:
2311:
2310:
2298:
2297:
2282:
2278:
2277:
2271:1536982932706676
2265:
2264:
2249:
2245:
2244:
2238:2059655218961613
2232:
2231:
2216:
2212:
2211:
2205:3058262831974168
2199:
2198:
2183:
2179:
2178:
2172:5726433061530961
2166:
2165:
2150:
2146:
2145:
2133:
2132:
2117:
2113:
2112:
2100:
2099:
2084:
2080:
2079:
2067:
2066:
2051:
2047:
2046:
2034:
2033:
2018:
2009:
1984:
1983:
1971:
1970:
1955:
1951:
1950:
1938:
1937:
1922:
1918:
1917:
1905:
1904:
1889:
1885:
1884:
1872:
1871:
1856:
1852:
1851:
1839:
1838:
1823:
1819:
1818:
1806:
1805:
1790:
1786:
1785:
1773:
1772:
1757:
1753:
1752:
1740:
1739:
1724:
1720:
1719:
1707:
1706:
1691:
1682:
1657:
1656:
1644:
1643:
1628:
1624:
1623:
1611:
1610:
1595:
1591:
1590:
1578:
1577:
1562:
1558:
1557:
1545:
1544:
1529:
1525:
1524:
1512:
1511:
1496:
1492:
1491:
1479:
1478:
1463:
1459:
1458:
1446:
1445:
1430:
1426:
1425:
1413:
1412:
1397:
1388:
1363:
1362:
1350:
1349:
1334:
1330:
1329:
1317:
1316:
1301:
1297:
1296:
1284:
1283:
1268:
1264:
1263:
1251:
1250:
1235:
1231:
1230:
1218:
1217:
1202:
1198:
1197:
1185:
1184:
1169:
1165:
1164:
1152:
1151:
1136:
1127:
1086:
1084:
1083:
1078:
1076:
1072:
1071:
1059:
1058:
1043:
1039:
1038:
1026:
1025:
1010:
1006:
1005:
993:
992:
977:
973:
972:
960:
959:
944:
940:
939:
927:
926:
911:
907:
906:
894:
893:
878:
869:
844:
843:
831:
830:
815:
811:
810:
798:
797:
782:
778:
777:
765:
764:
749:
745:
744:
732:
731:
716:
712:
711:
699:
698:
683:
674:
649:
648:
636:
635:
620:
616:
615:
603:
602:
587:
583:
582:
570:
569:
554:
550:
549:
537:
536:
521:
512:
487:
486:
474:
473:
458:
454:
453:
441:
440:
425:
421:
420:
408:
407:
392:
383:
358:
357:
345:
344:
329:
325:
324:
312:
311:
296:
287:
262:
261:
249:
248:
233:
224:
92:
90:
4071:
4070:
4066:
4065:
4064:
4062:
4061:
4060:
4041:
4040:
4024:
4004:
3996:
3899:
3898:
3896:
3803:
3798:
3791:
3787:
3778:
3774:
3767:
3763:
3756:
3752:
3747:
3743:
3738:
3734:
3719:10.2307/2324954
3697:
3696:
3692:
3687:Wayback Machine
3678:
3674:
3658:
3657:
3653:
3640:
3639:
3635:
3622:
3621:
3617:
3613:
3608:
3574:
3542:
3527:
3513:
3512:
3502:
3489:
3480:
3479:
3469:
3456:
3447:
3446:
3436:
3423:
3414:
3413:
3403:
3390:
3383:
3371:
3370:
3352:
3351:
3341:
3328:
3319:
3318:
3308:
3295:
3286:
3285:
3275:
3262:
3255:
3243:
3242:
3232:
3228:
3220:
3212:
3208:
3194:
3190:
3183:
3165:
3164:
3154:
3141:
3132:
3131:
3121:
3108:
3099:
3098:
3088:
3075:
3066:
3065:
3055:
3042:
3033:
3032:
3022:
3009:
3000:
2999:
2989:
2976:
2967:
2966:
2956:
2943:
2934:
2933:
2923:
2910:
2901:
2900:
2890:
2877:
2868:
2867:
2857:
2844:
2835:
2834:
2824:
2811:
2802:
2801:
2791:
2778:
2769:
2768:
2760:
2739:
2738:
2728:
2715:
2706:
2705:
2695:
2682:
2673:
2672:
2662:
2649:
2640:
2639:
2629:
2616:
2607:
2606:
2596:
2583:
2574:
2573:
2563:
2550:
2541:
2540:
2530:
2517:
2508:
2507:
2497:
2484:
2475:
2474:
2464:
2451:
2442:
2441:
2431:
2418:
2409:
2408:
2398:
2385:
2376:
2375:
2367:
2346:
2345:
2337:391313741613522
2335:
2322:
2313:
2312:
2304:904069333568884
2302:
2289:
2280:
2279:
2269:
2256:
2247:
2246:
2236:
2223:
2214:
2213:
2203:
2190:
2181:
2180:
2170:
2157:
2148:
2147:
2137:
2124:
2115:
2114:
2104:
2091:
2082:
2081:
2071:
2058:
2049:
2048:
2038:
2025:
2016:
2015:
2007:
1986:
1985:
1975:
1962:
1953:
1952:
1942:
1929:
1920:
1919:
1909:
1896:
1887:
1886:
1876:
1863:
1854:
1853:
1843:
1830:
1821:
1820:
1810:
1797:
1788:
1787:
1777:
1764:
1755:
1754:
1744:
1731:
1722:
1721:
1711:
1698:
1689:
1688:
1680:
1659:
1658:
1648:
1635:
1626:
1625:
1615:
1602:
1593:
1592:
1582:
1569:
1560:
1559:
1549:
1536:
1527:
1526:
1516:
1503:
1494:
1493:
1483:
1470:
1461:
1460:
1450:
1437:
1428:
1427:
1417:
1404:
1395:
1394:
1386:
1365:
1364:
1354:
1341:
1332:
1331:
1321:
1308:
1299:
1298:
1288:
1275:
1266:
1265:
1255:
1242:
1233:
1232:
1222:
1209:
1200:
1199:
1189:
1176:
1167:
1166:
1156:
1143:
1134:
1133:
1125:
1098:
1097:
1092:
1074:
1073:
1063:
1050:
1041:
1040:
1030:
1017:
1008:
1007:
997:
984:
975:
974:
964:
951:
942:
941:
931:
918:
909:
908:
898:
885:
876:
875:
867:
846:
845:
835:
822:
813:
812:
802:
789:
780:
779:
769:
756:
747:
746:
736:
723:
714:
713:
703:
690:
681:
680:
672:
651:
650:
640:
627:
618:
617:
607:
594:
585:
584:
574:
561:
552:
551:
541:
528:
519:
518:
510:
489:
488:
478:
465:
456:
455:
445:
432:
423:
422:
412:
399:
390:
389:
381:
360:
359:
349:
336:
327:
326:
316:
303:
294:
293:
285:
264:
263:
253:
240:
231:
230:
222:
195:
194:
189:
123:
88:
84:
24:
17:
12:
11:
5:
4069:
4067:
4059:
4058:
4053:
4043:
4042:
4039:
4038:
4036:. Numberphile.
4022:
4017:
4015:. Numberphile.
4002:
3995:
3994:External links
3992:
3991:
3990:
3979:
3960:
3957:
3954:
3951:
3948:
3945:
3942:
3939:
3936:
3933:
3930:
3927:
3924:
3921:
3918:
3915:
3912:
3909:
3906:
3891:
3876:
3822:
3811:
3802:
3799:
3797:
3796:
3785:
3772:
3761:
3750:
3741:
3732:
3713:(4): 331–340.
3690:
3672:
3669:. Numberphile.
3651:
3633:
3614:
3612:
3609:
3607:
3606:
3603:Sums of powers
3600:
3594:
3588:
3583:
3577:
3568:
3562:
3556:
3550:
3543:
3541:
3538:
3509:
3505:
3501:
3496:
3492:
3488:
3485:
3483:
3481:
3476:
3472:
3468:
3463:
3459:
3455:
3452:
3450:
3448:
3443:
3439:
3435:
3430:
3426:
3422:
3419:
3417:
3415:
3410:
3406:
3402:
3397:
3393:
3389:
3386:
3384:
3382:
3379:
3378:
3348:
3344:
3340:
3335:
3331:
3327:
3324:
3322:
3320:
3315:
3311:
3307:
3302:
3298:
3294:
3291:
3289:
3287:
3282:
3278:
3274:
3269:
3265:
3261:
3258:
3256:
3254:
3251:
3250:
3207:, the numbers
3193:is written as
3182:
3179:
3161:
3157:
3153:
3148:
3144:
3140:
3137:
3135:
3133:
3128:
3124:
3120:
3115:
3111:
3107:
3104:
3102:
3100:
3095:
3091:
3087:
3082:
3078:
3074:
3071:
3069:
3067:
3062:
3058:
3054:
3049:
3045:
3041:
3038:
3036:
3034:
3029:
3025:
3021:
3016:
3012:
3008:
3005:
3003:
3001:
2996:
2992:
2988:
2983:
2979:
2975:
2972:
2970:
2968:
2963:
2959:
2955:
2950:
2946:
2942:
2939:
2937:
2935:
2930:
2926:
2922:
2917:
2913:
2909:
2906:
2904:
2902:
2897:
2893:
2889:
2884:
2880:
2876:
2873:
2871:
2869:
2864:
2860:
2856:
2851:
2847:
2843:
2840:
2838:
2836:
2831:
2827:
2823:
2818:
2814:
2810:
2807:
2805:
2803:
2798:
2794:
2790:
2785:
2781:
2777:
2774:
2772:
2770:
2767:
2761:
2759:
2756:
2753:
2750:
2747:
2744:
2741:
2740:
2735:
2731:
2727:
2722:
2718:
2714:
2711:
2709:
2707:
2702:
2698:
2694:
2689:
2685:
2681:
2678:
2676:
2674:
2669:
2665:
2661:
2656:
2652:
2648:
2645:
2643:
2641:
2636:
2632:
2628:
2623:
2619:
2615:
2612:
2610:
2608:
2603:
2599:
2595:
2590:
2586:
2582:
2579:
2577:
2575:
2570:
2566:
2562:
2557:
2553:
2549:
2546:
2544:
2542:
2537:
2533:
2529:
2524:
2520:
2516:
2513:
2511:
2509:
2504:
2500:
2496:
2491:
2487:
2483:
2480:
2478:
2476:
2471:
2467:
2463:
2458:
2454:
2450:
2447:
2445:
2443:
2438:
2434:
2430:
2425:
2421:
2417:
2414:
2412:
2410:
2405:
2401:
2397:
2392:
2388:
2384:
2381:
2379:
2377:
2374:
2368:
2366:
2363:
2360:
2357:
2354:
2351:
2348:
2347:
2342:
2338:
2334:
2329:
2325:
2321:
2318:
2316:
2314:
2309:
2305:
2301:
2296:
2292:
2288:
2285:
2283:
2281:
2276:
2272:
2268:
2263:
2259:
2255:
2252:
2250:
2248:
2243:
2239:
2235:
2230:
2226:
2222:
2219:
2217:
2215:
2210:
2206:
2202:
2197:
2193:
2189:
2186:
2184:
2182:
2177:
2173:
2169:
2164:
2160:
2156:
2153:
2151:
2149:
2144:
2140:
2136:
2131:
2127:
2123:
2120:
2118:
2116:
2111:
2107:
2103:
2098:
2094:
2090:
2087:
2085:
2083:
2078:
2074:
2070:
2065:
2061:
2057:
2054:
2052:
2050:
2045:
2041:
2037:
2032:
2028:
2024:
2021:
2019:
2017:
2014:
2008:
2006:
2003:
2000:
1997:
1994:
1991:
1988:
1987:
1982:
1978:
1974:
1969:
1965:
1964:51538406706318
1961:
1958:
1956:
1954:
1949:
1945:
1941:
1936:
1932:
1931:51530042142656
1928:
1925:
1923:
1921:
1916:
1912:
1908:
1903:
1899:
1898:51518075693259
1895:
1892:
1890:
1888:
1883:
1879:
1875:
1870:
1866:
1865:51471469037044
1862:
1859:
1857:
1855:
1850:
1846:
1845:15189477616793
1842:
1837:
1833:
1832:51094952419111
1829:
1826:
1824:
1822:
1817:
1813:
1812:28916052994804
1809:
1804:
1800:
1799:48305916483224
1796:
1793:
1791:
1789:
1784:
1780:
1779:31188298220688
1776:
1771:
1767:
1766:47409526164756
1763:
1760:
1758:
1756:
1751:
1747:
1746:32610071299666
1743:
1738:
1734:
1733:46756812032798
1730:
1727:
1725:
1723:
1718:
1714:
1713:40153439139764
1710:
1705:
1701:
1700:41632176837064
1697:
1694:
1692:
1690:
1687:
1681:
1679:
1676:
1673:
1670:
1667:
1664:
1661:
1660:
1655:
1651:
1647:
1642:
1638:
1634:
1631:
1629:
1627:
1622:
1618:
1614:
1609:
1605:
1601:
1598:
1596:
1594:
1589:
1585:
1581:
1576:
1572:
1568:
1565:
1563:
1561:
1556:
1552:
1548:
1543:
1539:
1535:
1532:
1530:
1528:
1523:
1519:
1515:
1510:
1506:
1502:
1499:
1497:
1495:
1490:
1486:
1482:
1477:
1473:
1469:
1466:
1464:
1462:
1457:
1453:
1449:
1444:
1440:
1436:
1433:
1431:
1429:
1424:
1420:
1416:
1411:
1407:
1403:
1400:
1398:
1396:
1393:
1387:
1385:
1382:
1379:
1376:
1373:
1370:
1367:
1366:
1361:
1357:
1353:
1348:
1344:
1340:
1337:
1335:
1333:
1328:
1324:
1320:
1315:
1311:
1307:
1304:
1302:
1300:
1295:
1291:
1287:
1282:
1278:
1274:
1271:
1269:
1267:
1262:
1258:
1254:
1249:
1245:
1241:
1238:
1236:
1234:
1229:
1225:
1221:
1216:
1212:
1208:
1205:
1203:
1201:
1196:
1192:
1188:
1183:
1179:
1175:
1172:
1170:
1168:
1163:
1159:
1155:
1150:
1146:
1142:
1139:
1137:
1135:
1132:
1126:
1124:
1121:
1118:
1115:
1112:
1109:
1106:
1105:
1091:
1088:
1070:
1066:
1062:
1057:
1053:
1049:
1046:
1044:
1042:
1037:
1033:
1029:
1024:
1020:
1016:
1013:
1011:
1009:
1004:
1000:
996:
991:
987:
983:
980:
978:
976:
971:
967:
963:
958:
954:
950:
947:
945:
943:
938:
934:
930:
925:
921:
917:
914:
912:
910:
905:
901:
897:
892:
888:
884:
881:
879:
877:
874:
868:
866:
863:
860:
857:
854:
851:
848:
847:
842:
838:
834:
829:
825:
821:
818:
816:
814:
809:
805:
801:
796:
792:
788:
785:
783:
781:
776:
772:
768:
763:
759:
755:
752:
750:
748:
743:
739:
735:
730:
726:
722:
719:
717:
715:
710:
706:
702:
697:
693:
689:
686:
684:
682:
679:
673:
671:
668:
665:
662:
659:
656:
653:
652:
647:
643:
639:
634:
630:
626:
623:
621:
619:
614:
610:
606:
601:
597:
593:
590:
588:
586:
581:
577:
573:
568:
564:
560:
557:
555:
553:
548:
544:
540:
535:
531:
527:
524:
522:
520:
517:
511:
509:
506:
503:
500:
497:
494:
491:
490:
485:
481:
477:
472:
468:
464:
461:
459:
457:
452:
448:
444:
439:
435:
431:
428:
426:
424:
419:
415:
411:
406:
402:
398:
395:
393:
391:
388:
382:
380:
377:
374:
371:
368:
365:
362:
361:
356:
352:
348:
343:
339:
335:
332:
330:
328:
323:
319:
315:
310:
306:
302:
299:
297:
295:
292:
286:
284:
281:
278:
275:
272:
269:
266:
265:
260:
256:
252:
247:
243:
239:
236:
234:
232:
229:
223:
221:
218:
215:
212:
209:
206:
203:
202:
188:
185:
177:cabtaxi number
122:
119:
95:mathematicians
55:taxicab number
21:Taxi medallion
15:
13:
10:
9:
6:
4:
3:
2:
4068:
4057:
4054:
4052:
4051:Number theory
4049:
4048:
4046:
4035:
4031:
4027:
4023:
4021:
4018:
4014:
4013:
4008:
4003:
4001:
3998:
3997:
3993:
3988:
3984:
3980:
3977:
3973:
3955:
3949:
3946:
3940:
3934:
3931:
3925:
3919:
3916:
3910:
3904:
3892:
3889:
3885:
3881:
3877:
3874:
3870:
3867:
3863:
3859:
3855:
3851:
3847:
3843:
3839:
3835:
3831:
3827:
3823:
3820:
3816:
3812:
3809:
3805:
3804:
3800:
3794:
3789:
3786:
3782:
3776:
3773:
3770:
3765:
3762:
3759:
3754:
3751:
3745:
3742:
3736:
3733:
3728:
3724:
3720:
3716:
3712:
3708:
3704:
3700:
3694:
3691:
3688:
3684:
3681:
3676:
3673:
3668:
3667:
3662:
3655:
3652:
3647:
3643:
3637:
3634:
3629:
3625:
3619:
3616:
3610:
3604:
3601:
3598:
3595:
3592:
3589:
3587:
3584:
3581:
3578:
3572:
3569:
3566:
3563:
3560:
3557:
3554:
3551:
3548:
3547:1729 (number)
3545:
3544:
3539:
3537:
3535:
3530:
3507:
3503:
3499:
3494:
3490:
3486:
3484:
3474:
3470:
3466:
3461:
3457:
3453:
3451:
3441:
3437:
3433:
3428:
3424:
3420:
3418:
3408:
3404:
3400:
3395:
3391:
3387:
3385:
3380:
3368:
3365:
3346:
3342:
3338:
3333:
3329:
3325:
3323:
3313:
3309:
3305:
3300:
3296:
3292:
3290:
3280:
3276:
3272:
3267:
3263:
3259:
3257:
3252:
3240:
3238:
3224:
3218:
3205:
3201:
3197:
3188:
3180:
3178:
3159:
3155:
3151:
3146:
3142:
3138:
3136:
3126:
3122:
3118:
3113:
3109:
3105:
3103:
3093:
3089:
3085:
3080:
3076:
3072:
3070:
3060:
3056:
3052:
3047:
3043:
3039:
3037:
3027:
3023:
3019:
3014:
3010:
3006:
3004:
2994:
2990:
2986:
2981:
2977:
2973:
2971:
2961:
2957:
2953:
2948:
2944:
2940:
2938:
2928:
2924:
2920:
2915:
2911:
2907:
2905:
2895:
2891:
2887:
2882:
2878:
2874:
2872:
2862:
2858:
2854:
2849:
2845:
2841:
2839:
2829:
2825:
2821:
2816:
2812:
2808:
2806:
2796:
2792:
2788:
2783:
2779:
2775:
2773:
2765:
2757:
2751:
2745:
2742:
2733:
2729:
2725:
2720:
2716:
2712:
2710:
2700:
2696:
2692:
2687:
2683:
2679:
2677:
2667:
2663:
2659:
2654:
2650:
2646:
2644:
2634:
2630:
2626:
2621:
2617:
2613:
2611:
2601:
2597:
2593:
2588:
2584:
2580:
2578:
2568:
2564:
2560:
2555:
2551:
2547:
2545:
2535:
2531:
2527:
2522:
2518:
2514:
2512:
2502:
2498:
2494:
2489:
2485:
2481:
2479:
2469:
2465:
2461:
2456:
2452:
2448:
2446:
2436:
2432:
2428:
2423:
2419:
2415:
2413:
2403:
2399:
2395:
2390:
2386:
2382:
2380:
2372:
2364:
2358:
2352:
2349:
2340:
2336:
2332:
2327:
2323:
2319:
2317:
2307:
2303:
2299:
2294:
2290:
2286:
2284:
2274:
2270:
2266:
2261:
2257:
2253:
2251:
2241:
2237:
2233:
2228:
2224:
2220:
2218:
2208:
2204:
2200:
2195:
2191:
2187:
2185:
2175:
2171:
2167:
2162:
2158:
2154:
2152:
2142:
2138:
2134:
2129:
2125:
2121:
2119:
2109:
2105:
2101:
2096:
2092:
2088:
2086:
2076:
2072:
2068:
2063:
2059:
2055:
2053:
2043:
2039:
2035:
2030:
2026:
2022:
2020:
2012:
2004:
1998:
1992:
1989:
1980:
1977:1037967484386
1976:
1972:
1967:
1963:
1959:
1957:
1947:
1944:4076877805588
1943:
1939:
1934:
1930:
1926:
1924:
1914:
1911:5463276442869
1910:
1906:
1901:
1897:
1893:
1891:
1881:
1878:8112103002584
1877:
1873:
1868:
1864:
1860:
1858:
1848:
1844:
1840:
1835:
1831:
1827:
1825:
1815:
1811:
1807:
1802:
1798:
1794:
1792:
1782:
1778:
1774:
1769:
1765:
1761:
1759:
1749:
1745:
1741:
1736:
1732:
1728:
1726:
1716:
1712:
1708:
1703:
1699:
1695:
1693:
1685:
1677:
1671:
1665:
1662:
1653:
1649:
1645:
1640:
1636:
1632:
1630:
1620:
1616:
1612:
1607:
1603:
1599:
1597:
1587:
1583:
1579:
1574:
1570:
1566:
1564:
1554:
1550:
1546:
1541:
1537:
1533:
1531:
1521:
1517:
1513:
1508:
1504:
1500:
1498:
1488:
1484:
1480:
1475:
1471:
1467:
1465:
1455:
1451:
1447:
1442:
1438:
1434:
1432:
1422:
1418:
1414:
1409:
1405:
1401:
1399:
1391:
1383:
1377:
1371:
1368:
1359:
1355:
1351:
1346:
1342:
1338:
1336:
1326:
1322:
1318:
1313:
1309:
1305:
1303:
1293:
1289:
1285:
1280:
1276:
1272:
1270:
1260:
1256:
1252:
1247:
1243:
1239:
1237:
1227:
1223:
1219:
1214:
1210:
1206:
1204:
1194:
1190:
1186:
1181:
1177:
1173:
1171:
1161:
1157:
1153:
1148:
1144:
1140:
1138:
1130:
1122:
1116:
1110:
1107:
1095:
1089:
1087:
1068:
1064:
1060:
1055:
1051:
1047:
1045:
1035:
1031:
1027:
1022:
1018:
1014:
1012:
1002:
998:
994:
989:
985:
981:
979:
969:
965:
961:
956:
952:
948:
946:
936:
932:
928:
923:
919:
915:
913:
903:
899:
895:
890:
886:
882:
880:
872:
864:
858:
852:
849:
840:
836:
832:
827:
823:
819:
817:
807:
803:
799:
794:
790:
786:
784:
774:
770:
766:
761:
757:
753:
751:
741:
737:
733:
728:
724:
720:
718:
708:
704:
700:
695:
691:
687:
685:
677:
669:
663:
657:
654:
645:
641:
637:
632:
628:
624:
622:
612:
608:
604:
599:
595:
591:
589:
579:
575:
571:
566:
562:
558:
556:
546:
542:
538:
533:
529:
525:
523:
516:6963472309248
515:
507:
501:
495:
492:
483:
479:
475:
470:
466:
462:
460:
450:
446:
442:
437:
433:
429:
427:
417:
413:
409:
404:
400:
396:
394:
386:
378:
372:
366:
363:
354:
350:
346:
341:
337:
333:
331:
321:
317:
313:
308:
304:
300:
298:
290:
282:
276:
270:
267:
258:
254:
250:
245:
241:
237:
235:
227:
219:
213:
207:
204:
192:
186:
184:
182:
178:
174:
170:
165:
162:
157:
155:
151:
147:
144:
140:
136:
132:
128:
120:
117:
115:
111:
105:
103:
99:
96:
87:
81:
79:
75:
71:
70:integer cubes
68:
64:
61:) or Taxicab(
60:
56:
52:
48:
40:
36:
32:
28:
22:
4030:Haran, Brady
4026:Singh, Simon
4011:
4007:Haran, Brady
3986:
3982:
3975:
3894:
3883:
3879:
3861:
3857:
3853:
3849:
3845:
3841:
3837:
3833:
3829:
3825:
3818:
3814:
3807:
3788:
3775:
3764:
3753:
3744:
3735:
3710:
3706:
3693:
3675:
3665:
3661:Haran, Brady
3654:
3645:
3636:
3627:
3618:
3369:
3366:
3241:
3222:
3203:
3199:
3195:
3184:
1637:370779904362
1604:370633638081
1571:370298338396
1551:109276817387
1538:367589585749
1518:208029158236
1505:347524579016
1485:224376246192
1472:341075727804
1452:234604829494
1439:336379942682
1419:288873662876
1406:299512063576
1096:
1093:
193:
190:
172:
166:
158:
153:
149:
145:
139:E. M. Wright
124:
107:
85:
82:
73:
66:
62:
58:
54:
50:
44:
34:
3253:15170835645
1617:39304147071
1584:58360453256
135:G. H. Hardy
98:G. H. Hardy
47:mathematics
39:G. H. Hardy
4045:Categories
3813:J. Leech,
3801:References
3526:(sequence
3237:Paul Vojta
1650:7467391974
1343:2919526806
1310:2918375103
1277:2915734948
1244:2894406187
1224:1638024868
1211:2736414008
1191:1766742096
1178:2685635652
1158:1847282122
1145:2648660966
161:John Leech
93:involving
2758:≤
2746:
2365:≤
2353:
2005:≤
1993:
1678:≤
1666:
1384:≤
1372:
1323:309481473
1290:459531128
1257:860447381
1123:≤
1111:
853:
658:
496:
367:
271:
208:
3701:(1993).
3683:Archived
3540:See also
3215:must be
3187:cubefree
1356:58798362
1065:26224366
1052:18289922
1032:26590452
1019:17492496
999:27093208
986:16218068
966:28657487
933:28894803
900:28906206
387:87539319
169:summands
143:integers
67:positive
4032:(ed.).
4009:(ed.).
3971:
3897:
3869:1125858
3727:2324954
3663:(ed.).
3532:in the
3529:A080642
3504:1165884
3471:1207602
3438:1216102
3405:1216500
953:8519281
920:3064173
89:
35:picture
3888:online
3873:online
3725:
3491:600259
3458:341995
3425:136635
2763:
2370:
2010:
1683:
1389:
1128:
887:582162
870:
837:331954
824:231518
804:336588
791:221424
771:342952
758:205292
738:362753
725:107839
705:365757
675:
513:
384:
288:
225:
110:Putney
49:, the
3723:JSTOR
3611:Notes
3392:92227
3233:Ta(2)
3229:Ta(1)
692:38787
642:16630
629:13322
609:18072
596:10200
576:18948
543:19083
3534:OEIS
3343:2152
3330:1733
3310:2456
3277:2468
3231:and
3211:and
563:5436
530:2421
291:1729
137:and
114:1729
100:and
91:1919
78:1729
3860:,
3715:doi
3711:100
3536:).
3297:709
3264:517
3221:Ta(
480:414
467:255
447:423
434:228
414:436
401:167
156:).
86:ca.
72:in
53:th
45:In
4047::
4028:.
3974:,
3882:,
3871:,
3866:MR
3856:+
3852:=
3848:+
3844:=
3840:+
3836:=
3832:+
3828:=
3817:,
3721:.
3709:.
3705:.
3644:.
3626:.
3202:+
3198:=
2752:12
2743:Ta
2359:11
2350:Ta
1999:10
1990:Ta
1663:Ta
1369:Ta
1108:Ta
850:Ta
655:Ta
493:Ta
364:Ta
351:10
318:12
268:Ta
205:Ta
3985:,
3959:)
3956:d
3953:(
3950:s
3947:+
3944:)
3941:c
3938:(
3935:r
3932:=
3929:)
3926:b
3923:(
3920:q
3917:+
3914:)
3911:a
3908:(
3905:p
3875:.
3858:n
3854:m
3850:v
3846:u
3842:w
3838:z
3834:y
3830:x
3729:.
3717::
3648:.
3630:.
3508:3
3500:+
3495:3
3487:=
3475:3
3467:+
3462:3
3454:=
3442:3
3434:+
3429:3
3421:=
3409:3
3401:+
3396:3
3388:=
3347:3
3339:+
3334:3
3326:=
3314:3
3306:+
3301:3
3293:=
3281:3
3273:+
3268:3
3260:=
3225:)
3223:n
3213:y
3209:x
3204:y
3200:x
3196:T
3191:T
3160:3
3152:+
3147:3
3139:=
3127:3
3119:+
3114:3
3106:=
3094:3
3086:+
3081:3
3073:=
3061:3
3053:+
3048:3
3040:=
3028:3
3020:+
3015:3
3007:=
2995:3
2987:+
2982:3
2974:=
2962:3
2954:+
2949:3
2941:=
2929:3
2921:+
2916:3
2908:=
2896:3
2888:+
2883:3
2875:=
2863:3
2855:+
2850:3
2842:=
2830:3
2822:+
2817:3
2809:=
2797:3
2789:+
2784:3
2776:=
2755:)
2749:(
2734:3
2726:+
2721:3
2713:=
2701:3
2693:+
2688:3
2680:=
2668:3
2660:+
2655:3
2647:=
2635:3
2627:+
2622:3
2614:=
2602:3
2594:+
2589:3
2581:=
2569:3
2561:+
2556:3
2548:=
2536:3
2528:+
2523:3
2515:=
2503:3
2495:+
2490:3
2482:=
2470:3
2462:+
2457:3
2449:=
2437:3
2429:+
2424:3
2416:=
2404:3
2396:+
2391:3
2383:=
2362:)
2356:(
2341:3
2333:+
2328:3
2320:=
2308:3
2300:+
2295:3
2287:=
2275:3
2267:+
2262:3
2254:=
2242:3
2234:+
2229:3
2221:=
2209:3
2201:+
2196:3
2188:=
2176:3
2168:+
2163:3
2155:=
2143:3
2135:+
2130:3
2122:=
2110:3
2102:+
2097:3
2089:=
2077:3
2069:+
2064:3
2056:=
2044:3
2036:+
2031:3
2023:=
2002:)
1996:(
1981:3
1973:+
1968:3
1960:=
1948:3
1940:+
1935:3
1927:=
1915:3
1907:+
1902:3
1894:=
1882:3
1874:+
1869:3
1861:=
1849:3
1841:+
1836:3
1828:=
1816:3
1808:+
1803:3
1795:=
1783:3
1775:+
1770:3
1762:=
1750:3
1742:+
1737:3
1729:=
1717:3
1709:+
1704:3
1696:=
1675:)
1672:9
1669:(
1654:3
1646:+
1641:3
1633:=
1621:3
1613:+
1608:3
1600:=
1588:3
1580:+
1575:3
1567:=
1555:3
1547:+
1542:3
1534:=
1522:3
1514:+
1509:3
1501:=
1489:3
1481:+
1476:3
1468:=
1456:3
1448:+
1443:3
1435:=
1423:3
1415:+
1410:3
1402:=
1381:)
1378:8
1375:(
1360:3
1352:+
1347:3
1339:=
1327:3
1319:+
1314:3
1306:=
1294:3
1286:+
1281:3
1273:=
1261:3
1253:+
1248:3
1240:=
1228:3
1220:+
1215:3
1207:=
1195:3
1187:+
1182:3
1174:=
1162:3
1154:+
1149:3
1141:=
1120:)
1117:7
1114:(
1069:3
1061:+
1056:3
1048:=
1036:3
1028:+
1023:3
1015:=
1003:3
995:+
990:3
982:=
970:3
962:+
957:3
949:=
937:3
929:+
924:3
916:=
904:3
896:+
891:3
883:=
865:=
862:)
859:6
856:(
841:3
833:+
828:3
820:=
808:3
800:+
795:3
787:=
775:3
767:+
762:3
754:=
742:3
734:+
729:3
721:=
709:3
701:+
696:3
688:=
670:=
667:)
664:5
661:(
646:3
638:+
633:3
625:=
613:3
605:+
600:3
592:=
580:3
572:+
567:3
559:=
547:3
539:+
534:3
526:=
508:=
505:)
502:4
499:(
484:3
476:+
471:3
463:=
451:3
443:+
438:3
430:=
418:3
410:+
405:3
397:=
379:=
376:)
373:3
370:(
355:3
347:+
342:3
338:9
334:=
322:3
314:+
309:3
305:1
301:=
283:=
280:)
277:2
274:(
259:3
255:1
251:+
246:3
242:1
238:=
228:2
220:=
217:)
214:1
211:(
173:n
154:n
146:n
74:n
63:n
59:n
51:n
41:.
33:(
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
