A273908 Integers z such that x^2 + y^4 = z^6 where x, y, z > 0, is soluble.

5, 15, 20, 34, 39, 41, 45, 55, 60, 65, 80, 85, 111, 125, 135, 136, 145, 150, 156, 164, 175, 180, 194, 219, 220, 240, 245, 255, 260, 265, 299, 306, 313, 320, 325, 340, 351, 353, 369, 371, 375, 405, 410, 444, 445, 455, 495, 500, 505, 514, 525, 540, 544

Offset: 1

Author

Altug Alkan, Jun 03 2016

Keywords

• nonn

Comments

A271576 is a subsequence.

Terms that are not in A271576 are 55, 220, 299, ...

Sequence is infinite since if k is a term then also t^2*k is a term, for every t>0. - Giovanni Resta, Jun 04 2016

Examples

			5 is a term because 75^2 + 10^4 = 5^6.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A111925, A266212, A271576.

Programs

Mathematica

q[n_] := {} != Select[Range[n^(1/4)]^4, n > # && IntegerQ@ Sqrt[n - #] &]; Select[ Range[100], q[#^6] &] (* Giovanni Resta, Jun 04 2016 *)