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

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, 37, 39, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 57, 59, 60, 61, 63, 65, 67, 68, 69, 71, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 99, 100, 101, 103, 105

Offset: 1

Author

N. J. A. Sloane, Oct 29 2010

Keywords

• nonn
• easy

Links

• Aviezri S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (1) (2012) 42-46.

Crossrefs

Complement of A171945. Apart from initial term, same as A053661.

Programs

Maple

A17194X_list := proc(lim, X)
local n, d, S, A;
S := {1}; A := NULL;
for n from 1 to lim do
  d := numtheory[divisors](n);
  if d minus S <> {n} then
     A := A,`if`(X=5,n,iquo(n,2));
     S := S union d;
  fi
od; A end:
# A17194X_list(lim,4) gives A171944_list(lim);
# A17194X_list(lim,5) gives A171945_list(lim).
- Peter Luschny, Dec 28 2010

Mathematica

lim = 210; S = {1}; A = {};
Do[d = Divisors[n]; If[Complement[d, S] != {n}, A = Append[A, Quotient[n, 2]]; S = Union[S, d]], {n, 1, lim}];
A (* Jean-François Alcover, Jul 11 2019, after Peter Luschny *)