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%I #24 Aug 18 2017 08:44:31
%S 1,3,7,9,13,19,21,25,27,31,37,39,43,49,57,61,63,67,73,75,79,81,91,93,
%T 97,103,109,111,117,121,127,129,133,139,147,151,157,163,169,171,175,
%U 181,183,189,193,199,201,211,217,219,223,225,229,237,241,243,247,259,271,273,277,279,283,289,291,301,307,309
%N Odd Löschian numbers.
%C Löschian numbers are numbers of the form x^2 + xy + y^2 for integers x, y; they can all be written in the form 4^e * m where e is a nonnegative integer and m is an odd Löschian number. - _Charles R Greathouse IV_, Jan 04 2016
%H Charles R Greathouse IV, <a href="/A266836/b266836.txt">Table of n, a(n) for n = 1..10000</a>
%H Joerg Arndt, <a href="https://arxiv.org/abs/1607.02433">Plane-filling curves on all uniform grids</a>, arXiv preprint arXiv:1607.02433 [math.CO], 2016.
%t fQ[n_] := Resolve[Exists[{x, y}, Reduce[n == x^2 + x y + y^2, {x, y}, Integers]]]; Select[2 Range@ 155 - 1, fQ] (* _Michael De Vlieger_, Jan 04 2016, after _Jean-François Alcover_ at A003136 *)
%o (PARI) is(n)=(n%2==1) && #bnfisintnorm(bnfinit(z^2+z+1), n);
%o (PARI) x='x+O('x^1000); p=eta(x)^3/eta(x^3); for(n=0, 999, if(polcoeff(p, n) != 0 && n%2==1, print1(n, ", "))) \\ _Altug Alkan_, Jan 04 2016
%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, if(t%2, listput(v, t)); y++)); Set(v) \\ _Charles R Greathouse IV_, Jul 05 2017
%Y Cf. Loeschian numbers: A003136 (all), A202822 (3*k+1), A260682 (6*k+1).
%K nonn
%O 1,2
%A _Joerg Arndt_, Jan 04 2016
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