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

%I A293691 #11 Oct 18 2017 21:35:34
%S A293691 17,365,745,1025,1753,7813,8177,11665,15641,16649,27289,58825,59189,
%T A293691 65537,66265,66637,81161,117665,118673,129313,183185,250001,250729,
%U A293691 265721,273533,324545,367649,531457,532465,596977,746497,762121,781441,864145,885781,886145
%N A293691 Numbers z such that x^2 + y^6 = z^2 (with positive integers x and y) and gcd(x, y, z) = 1.
%C A293691 Subsequence of A293690.
%H A293691 Chai Wah Wu, <a href="/A293691/b293691.txt">Table of n, a(n) for n = 1..10000</a>
%e A293691 15^2 + 2^6 = 17^2 and gcd(15, 2, 17) = 1, 17 is a term.
%e A293691 885416^2 + 33^6 = 886145^2 and gcd(885416, 33, 886145) = 1, 886145 is a term.
%t A293691 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
%Y A293691 Cf. A103156, A174115, A293690.
%K A293691 nonn
%O A293691 1,1
%A A293691 _XU Pingya_, Oct 14 2017