A217248 Numbers whose square is the sum of two nonnegative cubes.

0, 1, 3, 4, 8, 24, 27, 32, 64, 81, 98, 108, 125, 168, 192, 216, 228, 256, 312, 343, 375, 500, 512, 525, 588, 648, 671, 729, 784, 847, 864, 1000, 1014, 1029, 1183, 1225, 1261, 1323, 1331, 1344, 1372, 1536, 1728, 1824, 2048, 2187, 2197, 2496, 2646, 2744, 2888

Offset

1,3

Comments

Numbers N such that N^2 = x^3 + y^3 where x and y are nonnegative integers. First case with 2 solutions is 77976^2 = 228^3 + 1824^3 = 1026^3 + 1710^3, see A051302. - Zak Seidov, Mar 21 2013

Links

Chai Wah Wu, Table of n, a(n) for n = 1..5000

Example

312 is in the sequence because 312^2 = 2^3 + 46^3.

Mathematica

m = 2888; Sort[Reap[Do[If[IntegerQ[c = Sqrt[a^3 + b^3]], Sow[c]], {a, 0, m^(2/3)}, {b, a, (m^2 - a^3)^(1/3)}]][[2, 1]]] (* Zak Seidov, Mar 21 2013 *)

Prog

(R)
  y=c(); maxsol=3000 #All solutions <this value
  for(i in 0:(maxsol^(2/3))) for(j in i:((maxsol^2-i^3)^(1/3)))
      if(i<=j & 2*i^3<maxsol^2) if((sqrt(i^3+j^3)->x)==as.integer(x))y=c(y, x)
sort(y)
(PARI) is(n)=n*=n; for(k=ceil((n/2-.5)^(1/3)), (n+.5)^(1/3), if(ispower(n-k^3, 3), return(1))); 0 \\ Charles R Greathouse IV, Mar 20 2013

Crossrefs

This sequence with only positive (nonzero) cubes: A050801, and that sequence squared: A050802

A natural extension of the hypotenuse numbers A009003.

Sequence in context: A101932 A204521 A073313 * A168382 A155701 A353950

Adjacent sequences: A217245 A217246 A217247 * A217249 A217250 A217251

Keyword

nonn

Author

Christian N. K. Anderson & Kevin L. Schwartz, Mar 20 2013

Extensions

Offset and a(35) corrected and a(36)-a(51) from Giovanni Resta, Mar 20 2013

Status

approved