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%I #13 Jul 05 2017 13:32:32
%S 0,4,12,16,28,36,48,52,64,76,84,100,108,112,124,144,148,156,172,192,
%T 196,208,228,244,252,256,268,292,300,304,316,324,336,364,372,388,400,
%U 412,432,436,444,448,468,484,496,508,516,532,556,576,588,592,604,624,628,652,676
%N Even Löschian numbers.
%C Even numbers of the form x^2 - xy + y^2.
%H Charles R Greathouse IV, <a href="/A270248/b270248.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 2 * A270050(n) = 4 * A003136(n).
%e Even number 12 is a term because 12 = 2^2 + 2*2 + 2^2.
%t Select[Range[0, 680, 2], Resolve@ Exists[{x, y}, Reduce[# == (x^2 - x y + y^2), {x, y}, Integers]] &] (* _Michael De Vlieger_, Mar 15 2016 *)
%o (PARI) x='x+O('x^800); p=eta(x)^3/eta(x^3); for(n=0, 799, if(polcoeff(p, n) != 0 && n % 2 == 0, print1(n, ", ")));
%o (PARI) list(lim)=my(v=List(), y, t); forstep(x=0, sqrtint(lim\3), 2, my(y=x, t); while((t=x^2+x*y+y^2)<=lim, listput(v, t); y+=2)); Set(v) \\ _Charles R Greathouse IV_, Jul 05 2017
%Y Cf. Loeschian numbers: A003136 (all), A266836 (2*k+1), A202822 (3*k+1), A260682 (6*k+1).
%K nonn
%O 1,2
%A _Altug Alkan_, Mar 14 2016