A271826 - OEIS

%I #18 Apr 19 2016 16:26:37

%S 6,9,15,27,48,53,59,71,72,78,84,87,90,96,98,100,116,120,121,125,134,

%T 153,162,163,167,180,188,204,213,215,216,224,225,226,230,240,242,243,

%U 244,251,253,255,262,264,279,280,287,288,289,303,314,324,330,342

%N Integers n such that n^2 = x^3 + y^3 + z^3, where x, y, z are positive integers, is soluble.

%C Intersection of A000290 and A003072.

%C Corresponding squares are 36, 81, 225, 729, 2304, 2809, 3481, 5041, ...

%C A165454 is a subsequence.

%C Terms that are not listed in A165454 are 9, 72, 100, 215, 243, 279, 289, ...

%e 6 is a term because 6^2 = 1^3 + 2^3 + 3^3.

%e 9 is a term because 9^2 = 3^3 + 3^3 + 3^3.

%e 15 is a term because 15^2 = 1^3 + 2^3 + 6^3.

%o (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);

%Y Cf. A000290, A003072, A112474, A165454.

%K nonn,easy

%O 1,1

%A _Altug Alkan_, Apr 15 2016