A271826 Integers n such that n^2 = x^3 + y^3 + z^3, where x, y, z are positive integers, is soluble.
6, 9, 15, 27, 48, 53, 59, 71, 72, 78, 84, 87, 90, 96, 98, 100, 116, 120, 121, 125, 134, 153, 162, 163, 167, 180, 188, 204, 213, 215, 216, 224, 225, 226, 230, 240, 242, 243, 244, 251, 253, 255, 262, 264, 279, 280, 287, 288, 289, 303, 314, 324, 330, 342
Offset: 1
Examples
6 is a term because 6^2 = 1^3 + 2^3 + 3^3. 9 is a term because 9^2 = 3^3 + 3^3 + 3^3. 15 is a term because 15^2 = 1^3 + 2^3 + 6^3.
Programs
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PARI
list(lim) = my(v=List(), k, t); lim\=1; for(x=1, sqrtnint(lim-2, 3), for(y=1, min(sqrtnint(lim-x^3-1, 3), x), k=x^3+y^3; for(z=1, min(sqrtnint(lim-k, 3), y), if(issquare(k+z^3), listput(v, round(sqrt(k+z^3))))))); Set(v);
Comments