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%I #10 Oct 18 2017 21:35:44
%S 33,1094,2219,4097,6283,39063,40156,69985,78157,82221,148109,411772,
%T 412865,450834,524289,526475,602413,823575,827639,893527,1347831,
%U 2391485,2430547,2500001,2502187,2803256,3323543,4783001,4787065,5307257,7282969,8957953,9036077
%N Numbers z such that x^2 + y^7 = z^2 (with positive integers x and y) and gcd(x, y, z) = 1.
%C Subsequence of A293692.
%H Chai Wah Wu, <a href="/A293693/b293693.txt">Table of n, a(n) for n = 1..10000</a>
%e 31^2 + 2^7 = 33^2 and gcd(31, 2, 33) = 1, 33 is a term.
%e 8879827^2 + 60^7 = 9036077^2 and gcd(8879827, 60, 9036077) = 1, 9036077 is a term.
%t z={};Do[If[IntegerQ[(n^2 - y^7)^(1/2)] && GCD[y,n]==1,AppendTo[z,n]],{n,9.7*10^6},{y,(n^2 - 1)^(1/7)}];z
%Y Cf. A103156, A174115, A293284, A293692.
%K nonn
%O 1,1
%A _XU Pingya_, Oct 14 2017