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A136312 Cubes that are the sum of two or more consecutive positive squares.

%I A136312 #18 Jan 24 2016 16:42:32
%S A136312 103823,274625,781229961,10091699281,22425768000,1853614522304,
%T A136312 2277044900416,4708686519081,6168761704000,82312875000000,
%U A136312 235125028708361,259266910222125,269648738245125,291658484677013,980893000925279,1568173521032000,1816249897646729
%N A136312 Cubes that are the sum of two or more consecutive positive squares.
%H A136312 Chai Wah Wu, <a href="/A136312/b136312.txt">Table of n, a(n) for n = 1..45</a>
%e A136312 From _Donovan Johnson_, Aug 02 2013: (Start)
%e A136312 103823 = 47^3 = 22^2 +...+ 68^2
%e A136312 274625 = 65^3 = 90^2 +...+ 115^2
%e A136312 781229961 = 921^3 = 2115^2 +...+ 2276^2
%e A136312 10091699281 = 2161^3 = 989^2 +...+ 3149^2
%e A136312 22425768000 = 2820^3 = 261^2 +...+ 4067^2
%e A136312 1853614522304 = 12284^3 = 23017^2 +...+ 26087^2
%e A136312 2277044900416 = 13156^3 = 17354^2 +...+ 22930^2
%e A136312 4708686519081 = 16761^3 = 24978^2 +...+ 30971^2
%e A136312 6168761704000 = 18340^3 = 125090^2 +...+ 125482^2
%e A136312 82312875000000 = 43500^3 = 83868^2 +...+ 94235^2
%e A136312 235125028708361 = 61721^3 = 24079^2 +...+ 89600^2
%e A136312 259266910222125 = 63765^3 = 64791^2 +...+ 101632^2
%e A136312 269648738245125 = 64605^3 = 248058^2 +...+ 252364^2
%e A136312 291658484677013 = 66317^3 = 189432^2 +...+ 197233^2
%e A136312 980893000925279 = 99359^3 = 45450^2 +...+ 144808^2
%e A136312 1568173521032000 = 116180^3 = 239806^2 +...+ 264454^2
%e A136312 1816249897646729 = 122009^3 = 279608^2 +...+ 301138^2 (End)
%e A136312 From _Chai Wah Wu_, Jan 16 2016: (Start)
%e A136312 3164933091345661 = 146821^3 = 77289^2 +...+ 215130^2
%e A136312 4047882458821811 = 159371^3 = 84755^2 +...+ 233631^2
%e A136312 17609483239992125 = 260165^3 = 254786^2 +...+ 410884^2
%e A136312 19593033022705472 = 269588^3 = 250354^2 +...+ 420721^2
%e A136312 31231769524613559 = 314919^3 = 927208^2 +...+ 962198^2
%e A136312 65514186944297000 = 403130^3 = 1033993^2 +...+ 1091959^2
%e A136312 143956092348157375 = 524095^3 = 1015471^2 +...+ 1139347^2
%e A136312 329053482838576341 = 690381^3 = 52911^2 +...+ 995751^2
%e A136312 538042267367704000 = 813340^3 = 733892^2 +...+ 1261891^2
%e A136312 566038214864690329 = 827209^3 = 2312937^2 +...+ 2414242^2
%e A136312 656781041834164521 = 869241^3 = 772114^2 +...+ 1344540^2
%e A136312 958188654740652544 = 985864^3 = 838168^2 +...+ 1512983^2
%e A136312 1741057552217028375 = 1203015^3 = 2665648^2 +...+ 2891070^2
%e A136312 2453606982838035081 = 1348761^3 = 2465960^2 +...+ 2817081^2
%e A136312 7324939312836848704 = 1942084^3 = 772001^2 +...+ 2820383^2
%e A136312 31128405637777584128 = 3145712^3 = 12484417^2 +...+ 12681023^2
%e A136312 47930487637898407256 = 3632486^3 = 7350251^2 +...+ 8147761^2
%e A136312 57859343297173518625 = 3867745^3 = 37789066^2 +...+ 37829539^2
%e A136312 58047677333527653953 = 3871937^3 = 12618972^2 +...+ 12973453^2
%e A136312 95340837894501722977 = 4568353^3 = 2089689^2 +...+ 6658041^2
%e A136312 115237534945436189000 = 4866290^3 = 530792^2 +...+ 7019416^2
%e A136312 192722849299621656989 = 5776229^3 = 6484162^2 +...+ 9475619^2
%e A136312 357785493772998213000 = 7099170^3 = 7766186^2 +...+ 11552409^2
%e A136312 595861293215117277369 = 8414889^3 = 17896962^2 +...+ 19591724^2
%e A136312 1040700726329018473909 = 10133869^3 = 26869573^2 +...+ 28239958^2
%e A136312 2330938094537294907904 = 13258984^3 = 2662775^2 +...+ 19139958^2
%e A136312 5464432352858170025529 = 17613609^3 = 31917186^2 +...+ 36570028^2
%e A136312 6591770507847656234375 = 18749975^3 = 93374626^2 +...+ 94124624^2
%e A136312 (End)
%o A136312 (PARI) find(lim)=my(t,v=List());for(k=2,(3*lim)^(1/3),t=k*(k-1)*(2*k-1)/6;for(n=k,(k-1)/2+sqrt(lim/k-(k^2-1)/12),if(ispower(t+=n^2-(n-k)^2,3),listput(v,t))));vecsort(Vec(v),,8) \\ _Charles R Greathouse IV_, Jun 11 2011
%Y A136312 Cf. A131643, A000578, A000290.
%K A136312 nonn
%O A136312 1,1
%A A136312 _Donovan Johnson_, Mar 23 2008
%E A136312 Edited definition and a(11)-a(14) from _Donovan Johnson_, Oct 01 2010
%E A136312 a(15)-a(16) from _Donovan Johnson_, Jun 11 2011
%E A136312 a(17) from _Donovan Johnson_, Aug 02 2013