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A272174 Values of a^3 + b^3 such that the equation a^3 + b^3 = x^2 + y^2 + z^2 is not soluble where a, b > 0 and x, y, z >= 0.

%I A272174 #6 Apr 24 2016 12:50:46
%S A272174 28,351,407,559,855,1008,1343,1792,2071,3087,3383,3439,3591,3887,4375,
%T A272174 4439,5103,5488,6119,6175,7471,8343,9207,10864,10991,11375,11772,
%U A272174 12175,12231,12383,12636,12679,13167,13895,14023,14167,14364,14911,16263,16956,17199,17919,17999
%N A272174 Values of a^3 + b^3 such that the equation a^3 + b^3 = x^2 + y^2 + z^2 is not soluble where a, b > 0 and x, y, z >= 0.
%C A272174 Intersection of A003325 and A004215.
%e A272174 28 is a term because 28 = 1^3 + 3^3 and 28 is the sum of 4 but no fewer nonzero squares.
%o A272174 (PARI) isA004215(n) = {local(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri -7 ; if( j % 8 ==0, return(1) ) ; ) ; fouri *= 4 ; ) ; return(0);}
%o A272174 isA003325(n) = {for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));}
%o A272174 lista(nn) = for(n=1, nn, if(isA004215(n) && isA003325(n), print1(n, ", ")));
%Y A272174 Cf. A003325, A004215, A267702.
%K A272174 nonn,easy
%O A272174 1,1
%A A272174 _Altug Alkan_, Apr 21 2016