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

1,2

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A028594 A239050 A152680 * A228274 A353793 A273501

Adjacent sequences: A270245 A270246 A270247 * A270249 A270250 A270251

Keyword

nonn

Author

Altug Alkan, Mar 14 2016

Status

approved