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A171944 N-positions for game of misere version of Mark.

%I A171944 #15 Jul 11 2019 14:44:35
%S A171944 0,2,3,5,7,8,9,11,12,13,15,17,19,20,21,23,25,27,28,29,31,32,33,35,36,
%T A171944 37,39,41,43,44,45,47,48,49,51,52,53,55,57,59,60,61,63,65,67,68,69,71,
%U A171944 73,75,76,77,79,80,81,83,84,85,87,89,91,92,93,95,97,99,100,101,103,105
%N A171944 N-positions for game of misere version of Mark.
%H A171944 Aviezri S. Fraenkel, <a href="http://dx.doi.org/10.1016/j.disc.2011.03.032">The vile, dopey, evil and odious game players</a>, Discrete Math. 312 (1) (2012) 42-46.
%p A171944 A17194X_list := proc(lim, X)
%p A171944 local n, d, S, A;
%p A171944 S := {1}; A := NULL;
%p A171944 for n from 1 to lim do
%p A171944   d := numtheory[divisors](n);
%p A171944   if d minus S <> {n} then
%p A171944      A := A,`if`(X=5,n,iquo(n,2));
%p A171944      S := S union d;
%p A171944   fi
%p A171944 od; A end:
%p A171944 # A17194X_list(lim,4) gives A171944_list(lim);
%p A171944 # A17194X_list(lim,5) gives A171945_list(lim).
%p A171944 - _Peter Luschny_, Dec 28 2010
%t A171944 lim = 210; S = {1}; A = {};
%t A171944 Do[d = Divisors[n]; If[Complement[d, S] != {n}, A = Append[A, Quotient[n, 2]]; S = Union[S, d]], {n, 1, lim}];
%t A171944 A (* _Jean-François Alcover_, Jul 11 2019, after _Peter Luschny_ *)
%Y A171944 Complement of A171945. Apart from initial term, same as A053661.
%K A171944 nonn,easy
%O A171944 1,2
%A A171944 _N. J. A. Sloane_, Oct 29 2010