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%I #9 Oct 06 2021 03:51:31
%S 8,256,1944,6655,8192,25000,35937,62208,134456,212960,262144,344605,
%T 453962,472392,692759,800000,1149984,1288408,1617165,1990656,2970344,
%U 4302592,6075000,6814720,8388608,8732691,11358856,14526784,15116544,19808792,20796875,22168288
%N Numbers k such that k^2 is the sum of two positive 5th powers.
%C If a^5 + b^5 = m, then (ma)^5 + (mb)^5 = m^6 = (m^3)^2 is square. Therefore A003347(n)^3 are terms of this sequence.
%C When k in this sequence, k * (n^5) (n = 2, 3, ... ) is also in this sequence.
%e 8^2 = 2^5 + 2^5, so 8 is in the sequence.
%e 6655^2 = 22^5 + 33^5, so 6655 is in the sequence.
%t lst={};Do[If[IntegerQ[(n^2-a^5)^(1/5)],AppendTo[lst,n^2]],{n,7000},{a,n^2/2)^(1/5)}]; lst
%Y Cf. A000404, A004431, A003325, A050801, A003336, A003347.
%K nonn
%O 1,1
%A _XU Pingya_, Sep 04 2017
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