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%I #16 Oct 14 2020 13:24:16
%S 6,15,27,48,53,59,71,78,84,87,90,96,98,116,120,121,125,134,153,162,
%T 163,167,180,188,204,213,216,224,225,226,230,240,242,244,251,253,255,
%U 262,264,280,287,288,303,314,324,330,342,350,356,363,368,372,381,384,393
%N Numbers the squares of which are sums of three distinct positive cubes.
%H Chai Wah Wu, <a href="/A165454/b165454.txt">Table of n, a(n) for n = 1..10000</a>
%F {k >0: k^2 in A024975}. [_R. J. Mathar_, Oct 06 2009]
%e 6 is in the sequence because 6^2 = 1^3+2^3+3^3.
%e 15 is in the sequence because 15^2 = 1^3+2^3+6^3.
%p N:= 1000: # to get all terms <= N
%p sc:= {seq(seq(seq(a^3 + b^3 + c^3, a = 1 .. min(b-1, floor((N^2 - b^3 - c^3)^(1/3)))), b = 2 .. min(c-1,floor((N^2 - c^3)^(1/3)))), c = 3 .. floor(N^(2/3)))}:
%p select(t -> member(t^2,sc), [$1..N]); # _Robert Israel_, Jan 27 2015
%t lst={};Do[Do[Do[d=Sqrt[a^3+b^3+c^3];If[d<=834&&IntegerQ[d],AppendTo[lst, d]],{c,b+1,5!,1}],{b,a+1,5!,1}],{a,5!}];Take[Union@lst,123]
%t Sqrt[# ]&/@Select[Total/@Subsets[Range[50]^3,{3}],IntegerQ[Sqrt[#]]&]// Union (* _Harvey P. Dale_, Oct 14 2020 *)
%Y Cf. A161992, A024973, A025399
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 20 2009
%E Comments moved to the examples by _R. J. Mathar_, Oct 07 2009
%E Title corrected by _Jeppe Stig Nielsen_, Jan 26 2015
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