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A134739 Cubes of (positive numbers that are not the sum of three nonzero squares), that is, the terms of A004214, cubed. 4

%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 e-mail 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(N-a^2-b^2))), b = a .. floor(sqrt(N-a^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(n-a^2-b^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

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Last modified January 18 04:45 EST 2019. Contains 319269 sequences. (Running on oeis4.)