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%I
%S 7,13,15,23,25,28,31,37,39,47,52,55,58,60,63,71,79,85,87,92,95,100,
%T 103,111,112,119,124,127,130,135,143,148,151,156,159,167,175,183,188,
%U 191,199,207,208,215,220,223,231,232,239,240,247,252,255,263,271,279,284
%N Numbers n such that n^2 is the sum of three nonzero squares while n is not.
%e 7 is a term because 7 is not in A000408 and 7^2 = 49 = 2^2 + 3^2 + 6^2.
%o (PARI) isA000408(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 lista(nn) = for(n=1, nn, if(!isA000408(n) && isA000408(n^2), print1(n, ", ")));
%Y Cf. A000408, A005767.
%K nonn,easy
%O 1,1
%A _Altug Alkan_, Jun 16 2016
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