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A270248
Even Löschian numbers.
2
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 14 2016
STATUS
approved