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%I #15 Jun 14 2016 04:19:24
%S 5,15,20,34,39,41,45,55,60,65,80,85,111,125,135,136,145,150,156,164,
%T 175,180,194,219,220,240,245,255,260,265,299,306,313,320,325,340,351,
%U 353,369,371,375,405,410,444,445,455,495,500,505,514,525,540,544
%N Integers z such that x^2 + y^4 = z^6 where x, y, z > 0, is soluble.
%C A271576 is a subsequence.
%C Terms that are not in A271576 are 55, 220, 299, ...
%C 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
%H Chai Wah Wu, <a href="/A273908/b273908.txt">Table of n, a(n) for n = 1..10000</a>
%e 5 is a term because 75^2 + 10^4 = 5^6.
%t q[n_] := {} != Select[Range[n^(1/4)]^4, n > # && IntegerQ@ Sqrt[n - #] &]; Select[ Range[100], q[#^6] &] (* _Giovanni Resta_, Jun 04 2016 *)
%Y Cf. A111925, A266212, A271576.
%K nonn
%O 1,1
%A _Altug Alkan_, Jun 03 2016
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