%I #36 Feb 26 2017 09:07:43
%S 0,1,3,4,8,24,27,32,64,81,98,108,125,168,192,216,228,256,312,343,375,
%T 500,512,525,588,648,671,729,784,847,864,1000,1014,1029,1183,1225,
%U 1261,1323,1331,1344,1372,1536,1728,1824,2048,2187,2197,2496,2646,2744,2888
%N Numbers whose square is the sum of two nonnegative cubes.
%C 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
%H Chai Wah Wu, <a href="/A217248/b217248.txt">Table of n, a(n) for n = 1..5000</a>
%e 312 is in the sequence because 312^2 = 2^3 + 46^3.
%t 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 *)
%o (R)
%o y=c(); maxsol=3000 #All solutions <this value
%o for(i in 0:(maxsol^(2/3))) for(j in i:((maxsol^2-i^3)^(1/3)))
%o if(i<=j & 2*i^3<maxsol^2) if((sqrt(i^3+j^3)->x)==as.integer(x))y=c(y,x)
%o sort(y)
%o (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
%Y This sequence with only positive (nonzero) cubes: A050801, and that sequence squared: A050802
%Y A natural extension of the hypotenuse numbers A009003.
%K nonn
%O 1,3
%A _Christian N. K. Anderson_ & _Kevin L. Schwartz_, Mar 20 2013
%E Offset and a(35) corrected and a(36)-a(51) from _Giovanni Resta_, Mar 20 2013