A293691 Numbers z such that x^2 + y^6 = z^2 (with positive integers x and y) and gcd(x, y, z) = 1.

17, 365, 745, 1025, 1753, 7813, 8177, 11665, 15641, 16649, 27289, 58825, 59189, 65537, 66265, 66637, 81161, 117665, 118673, 129313, 183185, 250001, 250729, 265721, 273533, 324545, 367649, 531457, 532465, 596977, 746497, 762121, 781441, 864145, 885781, 886145

Offset: 1

Author

XU Pingya, Oct 14 2017

Keywords

• nonn

Comments

Subsequence of A293690.

Examples

			15^2 + 2^6 = 17^2 and gcd(15, 2, 17) = 1, 17 is a term.
885416^2 + 33^6 = 886145^2 and gcd(885416, 33, 886145) = 1, 886145 is a term.
		

Links

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

Crossrefs

Cf. A103156, A174115, A293690.

Programs

Mathematica

z={};Do[If[IntegerQ[(n^2 - y^6)^(1/2)] && GCD[y,n]==1,AppendTo[z,n]],{n,8.9*10^5},{y,(n^2 - 1)^(1/6)}];z