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%I #6 Sep 03 2017 21:58:12
%S 8,1024,17496,131072,625000,2146689,2239488,6588344,16777216,38263752,
%T 80000000,155897368,74776192,86654464,501988136,843308032,1366875000,
%U 2147483648,3282709384,4694808843,4897760256,7150973912,10240000000,10474708672,12406605875
%N Numbers k such that k^5 is sum of two positive 7th powers.
%C When a^7 + b^7 = m, (m^2*a)^7 + (m^2*b)^7 = m^15 is 5th power.
%C When k in this sequence, k*(n^7) (n = 2, 3, ... ) is also in this sequence.
%e 8^5 = 4^7 + 4^7, so 8 is in the sequence.
%e 2146689^5 = 16641^7 + 33282^7, so 2146689 is in the sequence.
%t lst={};Do[If[IntegerQ[(n^5-a^7)^(1/7)],AppendTo[lst,n]],{n,1.3*10^10},{a,(n^5/2)^(1/7)}]; lst
%Y Cf. A000584, A001015, A000404, A009003, A050801.
%K nonn
%O 1,1
%A _XU Pingya_, Sep 03 2017
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