A270248 Even Löschian numbers.

0, 4, 12, 16, 28, 36, 48, 52, 64, 76, 84, 100, 108, 112, 124, 144, 148, 156, 172, 192, 196, 208, 228, 244, 252, 256, 268, 292, 300, 304, 316, 324, 336, 364, 372, 388, 400, 412, 432, 436, 444, 448, 468, 484, 496, 508, 516, 532, 556, 576, 588, 592, 604, 624, 628, 652, 676

Offset: 1

Author

Altug Alkan, Mar 14 2016

Keywords

• nonn

Comments

Even numbers of the form x^2 - xy + y^2.

Examples

			Even number 12 is a term because 12 = 2^2 + 2*2 + 2^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. Loeschian numbers: A003136 (all), A266836 (2*k+1), A202822 (3*k+1), A260682 (6*k+1).

Programs

Mathematica

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 *)

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, ", ")));

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

Formula

a(n) = 2 * A270050(n) = 4 * A003136(n).