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

103823, 274625, 781229961, 10091699281, 22425768000, 1853614522304, 2277044900416, 4708686519081, 6168761704000, 82312875000000, 235125028708361, 259266910222125, 269648738245125, 291658484677013, 980893000925279, 1568173521032000, 1816249897646729

Offset: 1

Author

Donovan Johnson, Mar 23 2008

Keywords

• nonn

Examples

			From _Donovan Johnson_, Aug 02 2013: (Start)
103823 = 47^3 = 22^2 +...+ 68^2
274625 = 65^3 = 90^2 +...+ 115^2
781229961 = 921^3 = 2115^2 +...+ 2276^2
10091699281 = 2161^3 = 989^2 +...+ 3149^2
22425768000 = 2820^3 = 261^2 +...+ 4067^2
1853614522304 = 12284^3 = 23017^2 +...+ 26087^2
2277044900416 = 13156^3 = 17354^2 +...+ 22930^2
4708686519081 = 16761^3 = 24978^2 +...+ 30971^2
6168761704000 = 18340^3 = 125090^2 +...+ 125482^2
82312875000000 = 43500^3 = 83868^2 +...+ 94235^2
235125028708361 = 61721^3 = 24079^2 +...+ 89600^2
259266910222125 = 63765^3 = 64791^2 +...+ 101632^2
269648738245125 = 64605^3 = 248058^2 +...+ 252364^2
291658484677013 = 66317^3 = 189432^2 +...+ 197233^2
980893000925279 = 99359^3 = 45450^2 +...+ 144808^2
1568173521032000 = 116180^3 = 239806^2 +...+ 264454^2
1816249897646729 = 122009^3 = 279608^2 +...+ 301138^2 (End)
From _Chai Wah Wu_, Jan 16 2016: (Start)
3164933091345661 = 146821^3 = 77289^2 +...+ 215130^2
4047882458821811 = 159371^3 = 84755^2 +...+ 233631^2
17609483239992125 = 260165^3 = 254786^2 +...+ 410884^2
19593033022705472 = 269588^3 = 250354^2 +...+ 420721^2
31231769524613559 = 314919^3 = 927208^2 +...+ 962198^2
65514186944297000 = 403130^3 = 1033993^2 +...+ 1091959^2
143956092348157375 = 524095^3 = 1015471^2 +...+ 1139347^2
329053482838576341 = 690381^3 = 52911^2 +...+ 995751^2
538042267367704000 = 813340^3 = 733892^2 +...+ 1261891^2
566038214864690329 = 827209^3 = 2312937^2 +...+ 2414242^2
656781041834164521 = 869241^3 = 772114^2 +...+ 1344540^2
958188654740652544 = 985864^3 = 838168^2 +...+ 1512983^2
1741057552217028375 = 1203015^3 = 2665648^2 +...+ 2891070^2
2453606982838035081 = 1348761^3 = 2465960^2 +...+ 2817081^2
7324939312836848704 = 1942084^3 = 772001^2 +...+ 2820383^2
31128405637777584128 = 3145712^3 = 12484417^2 +...+ 12681023^2
47930487637898407256 = 3632486^3 = 7350251^2 +...+ 8147761^2
57859343297173518625 = 3867745^3 = 37789066^2 +...+ 37829539^2
58047677333527653953 = 3871937^3 = 12618972^2 +...+ 12973453^2
95340837894501722977 = 4568353^3 = 2089689^2 +...+ 6658041^2
115237534945436189000 = 4866290^3 = 530792^2 +...+ 7019416^2
192722849299621656989 = 5776229^3 = 6484162^2 +...+ 9475619^2
357785493772998213000 = 7099170^3 = 7766186^2 +...+ 11552409^2
595861293215117277369 = 8414889^3 = 17896962^2 +...+ 19591724^2
1040700726329018473909 = 10133869^3 = 26869573^2 +...+ 28239958^2
2330938094537294907904 = 13258984^3 = 2662775^2 +...+ 19139958^2
5464432352858170025529 = 17613609^3 = 31917186^2 +...+ 36570028^2
6591770507847656234375 = 18749975^3 = 93374626^2 +...+ 94124624^2
(End)
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..45

Crossrefs

Cf. A131643, A000578, A000290.

Programs

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

Extensions

Edited definition and a(11)-a(14) from Donovan Johnson, Oct 01 2010

a(15)-a(16) from Donovan Johnson, Jun 11 2011

a(17) from Donovan Johnson, Aug 02 2013