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A271826
Integers n such that n^2 = x^3 + y^3 + z^3, where x, y, z are positive integers, is soluble.
0
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, ...
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
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Apr 15 2016
STATUS
approved