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

1,1

Links

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

Example

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)

Prog

(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

Crossrefs

Cf. A131643, A000578, A000290.

Sequence in context: A171162 A235721 A210180 * A205260 A076761 A236007

Adjacent sequences: A136309 A136310 A136311 * A136313 A136314 A136315

Keyword

nonn

Author

Donovan Johnson, Mar 23 2008

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

Status

approved