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Numbers k such that k^4 is the sum of two positive 5th powers.
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%I #6 Sep 11 2017 20:05:38

%S 16,512,3888,16384,50000,124416,268912,524288,944784,1185921,1600000,

%T 2576816,3981312,5940688,8605184,12150000,16777216,22717712,30233088,

%U 37949472,39617584,51200000,65345616,82458112,102981488,127401984,156250000,190102016,229582512

%N Numbers k such that k^4 is the sum of two positive 5th powers.

%C When a^5 + b^5 = m, (m^3 * a)^5 + (m^3 * b)^5 = m^16 is 4th power.

%C When k in this sequence, k * (n^5), for n > 1, is also in this sequence.

%e 16^4 = 8^5 + 8^5, so 16 is in the sequence.

%e 1185921^4 = 35937^5 + 71874^5, so 1185921 is in the sequence.

%t lst={};Do[If[IntegerQ[(n^4-a^5)^(1/5)],AppendTo[lst,n]],{n,2.3*10^8},{a,(n^4/2)^(1/5)}]; lst

%Y Cf. A000583, A000584, A000404, A009003, A050801.

%K nonn

%O 1,1

%A _XU Pingya_, Sep 04 2017