A171945 P-positions for game of misere version of Mark.

1, 4, 6, 10, 14, 16, 18, 22, 24, 26, 30, 34, 38, 40, 42, 46, 50, 54, 56, 58, 62, 64, 66, 70, 72, 74, 78, 82, 86, 88, 90, 94, 96, 98, 102, 104, 106, 110, 114, 118, 120, 122, 126, 130, 134, 136, 138, 142, 146, 150, 152, 154, 158, 160, 162, 166, 168, 170, 174

Offset: 1

Author

N. J. A. Sloane, Oct 29 2010

Keywords

• nonn
• easy

Comments

The same as A036554 except for the replacement of dopey by vile powers of 2. - Aviezri Fraenkel, Apr 28 2011

Links

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

Crossrefs

Complement of A171944. Also for n>1, twice A171944. Cf. A036554.

Programs

Maple

isA171944 := proc(n)
    option remember;
    if n =0 or n =2 then
        true;
    elif isA171945(n) then
        false;
    else
        true ;
    end if;
end proc:
isA171945 := proc(n)
    option remember;
    if n = 0 or n =2 then
        false ;
    elif n = 1 then
        true;
    elif n mod 2 <> 0 then
        return false;
    elif isA171944(n/2) then
        true;
    else
        false ;
    end if;
end proc:
for n from 0 to 400 do
    if isA171945(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Mar 28 2013

Mathematica

lim = 210; S = {1}; A = {};
Do[d = Divisors[n]; If[Complement[d, S] != {n}, A = Append[A, n]; S = Union[S, d]], {n, 1, lim}];
A (* Jean-François Alcover, Jul 11 2019, after Peter Luschny in A171944 *)