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Numbers that are primitively but not imprimitively represented by x^2+xy+y^2.
1

%I #13 Nov 10 2013 16:17:46

%S 0,1,3,7,13,19,21,31,37,39,43,57,61,67,73,79,91,93,97,103,109,111,127,

%T 129,133,139,151,157,163,181,183,193,199,201,211,217,219,223,229,237,

%U 241,247,259,271,273,277,283,291,301,307,309,313,327,331,337,349,367

%N Numbers that are primitively but not imprimitively represented by x^2+xy+y^2.

%C Also numbers that are squarefree and primitively represented by x^2+x*y+y^2. - _Frank M Jackson_, Nov 08 2013

%t lst = {}; Do[k=x^2+x*y+y^2; If[(SquareFreeQ[k] && GCD[x, y]==1) || k==0, AppendTo[lst, k]], {x, 0, 100}, {y, 0, x}]; Union@lst (* _Frank M Jackson_, Nov 08 2013 *)

%Y Cf. A034017, A003136, A045897.

%K nonn

%O 1,3

%A _N. J. A. Sloane_.

%E Extended by _Ray Chandler_, Jan 29 2009