%I
%S 1,8,64,125,343,512,1000,2197,3375,4096,8000,12167,15625,21952,29791,
%T 32768,50653,59319,64000,103823,140608,166375,195112,216000,250047,
%U 262144,357911,493039,512000,614125,658503,778688,857375,1000000
%N Cubes of (positive numbers that are not the sum of three nonzero squares), that is, the terms of A004214, cubed.
%C This sequence was inspired by email from _Ray Chandler_, Nov 07 2007.
%C Original name was: Cubes which are not the sum of three nonzero squares. That definition would not include 125 = 5^2 + 6^2 + 8^2.  _Robert Israel_, Jan 12 2016
%C For "(cubes of positive numbers) that are not the sum of three nonzero squares", that is, the cubes in A004214, see A267189.  _N. J. A. Sloane_, Jan 18 2016
%H Robert Israel, <a href="/A134739/b134739.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A004214(n)^3.  _Ray Chandler_, Jan 29 2009
%e 8 is in the sequence because it is not possible to express 2 as a sum of three nonzero squares and 2^3 = 8.
%e 27 is not in the sequence because 3 = 1^2 + 1^2 + 1^2.
%p N:= 1000: # to get all terms <= N^3
%p A004214:= {$1..N} minus {seq(seq(seq(a^2 + b^2 + c^2, c = b .. floor(sqrt(Na^2b^2))), b = a .. floor(sqrt(Na^2))),a=1..floor(sqrt(N/2)))}:
%p map(`^`,sort(convert(A004214,list)), 3); # _Robert Israel_, Jan 12 2016
%t searchMax = 16; Flatten[Position[Take[Rest[CoefficientList[Sum[x^(i^2), {i, searchMax}]^3, x]], searchMax^2], 0]]^3 (* Based on _Ray Chandler_'s program for A004214, _Alonso del Arte_, Jan 12 2016 *)
%o (PARI) is(n) = { my(a, b) ; a=1; while(a^2+1<n, b=1 ; while(b<=a && a^2+b^2<n, if(issquare(na^2b^2), return(1) ) ; b++ ; ) ; a++ ; ) ; return(0) ; }
%o for(n=1, 1e3, if(!is(n), print1(n^3, ", "))); \\ _Altug Alkan_, Jan 13 2016
%Y Cf. A004214, A134738, A267189.
%K nonn
%O 1,2
%A _Artur Jasinski_, Nov 07 2007
%E Definition corrected by _Robert Israel_, Jan 12 2016
