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Numbers k such that k^6 is sum of two positive 7th powers.
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%I #4 Sep 03 2017 21:58:18

%S 64,8192,139968,1048576,5000000,17915904,52706752,134217728,306110016,

%T 640000000,1247178944,2293235712,4015905088,6746464256,10935000000,

%U 17179869184,26261675072,39182082048,57207791296,81920000000,115269666624,159638904832,217908828608

%N Numbers k such that k^6 is sum of two positive 7th powers.

%C When a^7 + b^7 = m, (m^5*a)^7 + (m^5*b)^7 = m^36 is 6th power.

%C When k in this sequence, k*(n^7) (n = 2, 3, ... ) is also in this sequence.

%e 64^6 = 32^7 + 32^7, so 64 is in the sequence.

%e (5000000)^6 = (500000)^7 + (500000)^7, so 5000000 is in the sequence.

%t lst={};Do[If[IntegerQ[(n^6-a^7)^(1/7)],AppendTo[lst,n]],{n,2.9*10^11},{a,(n^6/2)^(1/7)}]; lst

%Y Cf. A001014, A001015, A000404, A009003, A050801.

%K nonn

%O 1,1

%A _XU Pingya_, Sep 03 2017