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

Author

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

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

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

A natural extension of the hypotenuse numbers A009003.

Programs

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 *)

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

R

y=c(); maxsol=3000 #All solutions x)==as.integer(x))y=c(y,x)
sort(y)

Extensions

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