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

1,1

Comments

Intersection of A000290 and A003072.

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

A165454 is a subsequence.

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

Links

Table of n, a(n) for n=1..54.

Example

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.

Prog

(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);

Crossrefs

Cf. A000290, A003072, A112474, A165454.

Sequence in context: A102971 A023885 A031209 * A242183 A300564 A316050

Adjacent sequences: A271823 A271824 A271825 * A271827 A271828 A271829

Keyword

nonn,easy

Author

Altug Alkan, Apr 15 2016

Status

approved