%I #21 Dec 16 2013 07:09:20
%S 2,4,5,6,8,9,10,11,12,14,15,16,17,18,20,22,23,24,25,26,27,28,29,30,32,
%T 33,34,35,36,38,40,41,42,44,45,46,47,48,50,51,52,53,54,55,56,58,59,60,
%U 62,63,64,65,66,68,69,70,71,72,74,75,76,77,78,80,81,82
%N Numbers that can't be written as x^2 + x*y + y^2, with 0 <= x <= y and gcd(x,y) = 1.
%C A000086(a(n)) = 0.
%C Also numbers n with psi(n) congruent to 0 mod 3, where psi is A001615, and also numbers divisible by 9 or by at least one prime of the form 3k-1: A003627. - _Enrique Pérez Herrero_, Dec 08 2013
%H Reinhard Zumkeller, <a href="/A226946/b226946.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[1000],Mod[# * Times@@(1+1/Transpose[FactorInteger[#]][[1]]),3]==0&] (* _Enrique Pérez Herrero_, Dec 08 2013 *)
%t nn = 10; lim = 1 + nn + nn^2; Complement[Range[2, lim], Select[Union[Flatten[Table[If[GCD[x, y] == 1, x^2 + x*y + y^2, 0], {y, nn}, {x, y}]]], # <= lim &]] (* _T. D. Noe_, Dec 09 2013 *)
%o (Haskell)
%o a226946 n = a226946_list !! (n-1)
%o a226946_list = filter ((== 0) . a000086) [1..]
%o -- _Reinhard Zumkeller_, Dec 16 2013, Jun 23 2013
%Y Cf. A034017 (complement).
%Y Cf. A003627, A001615.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jun 23 2013
%E The original definition was too weak; thanks to _T. D. Noe_ for having corrected this. - _Reinhard Zumkeller_, Dec 09 2013