This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A236300 #17 May 06 2014 06:33:57 %S A236300 8,9,16,18,20,27,28,32,35,36,40,44,45,49,52,54,56,63,64,65,68,70,72, %T A236300 76,77,80,81,88,90,91,92,98,99,100,104,108,112,116,117,119,124,125, %U A236300 126,128,130,133,135,136,140,143,144,148,152,153,154,160,161,162,164,169 %N A236300 Numbers n of the form x^3 + y^3 + z^3 - 3*x*y*z for x,y,z >= 0, where x + y + z < n. %C A236300 x^3 + y^3 + z^3 - 3*x*y*z = (x + y + z)*(x^2 + y^2 + z^2 - x*y - x*z - y*z), hence all terms are composite. %C A236300 From _Wolfdieter Lang_, Apr 30 2014: (Start) %C A236300 Take x >= y >= z >= 0, not all identical: the numbers are of the form (x + y + z)*(u^2 + v^2 + w^2)/2, where u = x-y, v = x-z, w = y-z, with u >= 0, v >=0, w >= 0, u - v + w = 0 and u^2 + v^2 + w^2 >= 4. %C A236300 (i) If, say, x = y but not equal to z, then the numbers are of the form (2*x+y)*(x-z)^2 with x-z >= 2, z >= 0. Similarly for the other case with y = z not equal to x. %C A236300 (ii) If x, y and z are distinct, u >= 1, v >= 1 and w >= 1, hence u is not equal to v, and v is not equal to w (because u - v + w = 0). (iia) If u = w then the numbers are of the form 3*y*3*(y-z)^2 with y-z >= 1, z >= 0. (iib) If the u, v, w are distinct >= 1 then the even members of the sequence A004432 with multiplicities A025442 are of interest. But only those (u, v, w) qualify which satisfy u - v + w = 0. E.g., A025442(5) = 30 = 1^2 + 2^2 + 5^2 does not qualify because no permutation of 1, 2, 5 works for u, v, w. A025442(1) = 14 qualifies because (u, v, w) = (2, 3, 1) satisfies 2 - 3 + 1 = 0. Then [x, y, z] = [4, 2, 1] and the number is 7*14/2 = 49. %C A236300 (End) %C A236300 The even numbers qualifying for the case (iib) above are shown in A240227 with the multiplicities A240228. - _Wolfdieter Lang_, May 02 2014 %e A236300 From _Wolfdieter Lang_, Apr 30 2014: (Start) %e A236300 The numbers of type (i) are seq((2*x+z)*(z-x)^2, z=0..(x-2)) (if x >= 2) and seq((2*x+z)*(z-x)^2, z >= (x+2)) for x = 0, 1, 2, ... E.g., x = 3: 54, 28, 44, and 108, 208, 350, 540, 784, 1088, 1458, 1900, 2420, 3024, ... %e A236300 The numbers of type (iia) are [seq(9*y*(y-z)^2, y >= 1+z)] for z = 0, 1, 2, ... E.g., z=3: 36, 180, 486, 1008, 1800, 2916, 4410, ... %e A236300 The numbers of type (iib) come from the even members 14, 26, 30, 38, 42, 46, 50, ... of A025442 (each with multiplicity 1) except of 30 (as explained above in a comment), 46 with 1, 3, 6 which is out, and also 50 with 3, 4, 5. 7*14/2 = 49 (see the comment above); 10*26/2 = 130 from (u, v, w) = (1, 4, 3) and [x, y, z] = [5, 4, 1]; 11*38/2 = 209 from (2, 5, 3) and [6, 4, 1]; 12*42/2 = 252 from (1, 5, 4) and [6, 5, 1]; ... %e A236300 (End) %Y A236300 Subsequence of A002808 (the composite numbers). A004432, A025442. %K A236300 nonn %O A236300 1,1 %A A236300 _Arkadiusz Wesolowski_, Apr 21 2014