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%I #12 Jul 05 2017 13:27:22
%S 0,3,9,12,21,27,36,39,48,57,63,75,81,84,93,108,111,117,129,144,147,
%T 156,171,183,189,192,201,219,225,228,237,243,252,273,279,291,300,309,
%U 324,327,333,336,351,363,372,381,387,399,417,432,441,444,453,468,471,489,507,513,516,525,543,549
%N Löschian numbers (A003136) that are multiples of 3.
%C Numbers of the form 3*(x^2 + xy + y^2).
%C Intersection of A008585 and A003136.
%H Charles R Greathouse IV, <a href="/A270672/b270672.txt">Table of n, a(n) for n = 1..10000</a>
%e 21 is a term because 21 = 3*7 = 4^2 + 4*1 + 1^2.
%t Select[Range[0, 600], Resolve[Exists[{x, y}, Reduce[# == 3 (x^2 + x y + y^2), {x, y}, Integers]]] &] (* _Michael De Vlieger_, Mar 21 2016 *)
%o (PARI) x='x+O('x^1000); p=eta(x)^3/eta(x^3); for(n=0, 999, if(polcoeff(p, n) != 0 && n % 3 == 0, print1(n, ", ")));
%o (PARI) list(lim)=my(v=List(), y, t); for(x=0, sqrtint(lim\3), my(y=x, t); while((t=x^2+x*y+y^2)<=lim, listput(v, t); y+=3)); Set(v) \\ _Charles R Greathouse IV_, Jul 05 2017
%Y Cf. Loeschian numbers: A003136 (all), A270248 (2*k), A266836 (2*k+1), A202822 (3*k+1), A260682 (6*k+1).
%K nonn
%O 1,2
%A _Altug Alkan_, Mar 21 2016
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