OFFSET
1,2
COMMENTS
The game is equivalent to the game of Nim with the additional allowed move consisting of removing one object from each pile.
MATHEMATICA
Clear[moves, los]; A003557[n_]:= {Module[{aux = FactorInteger[n], L=Length[FactorInteger[n]]}, Product[aux[[i, 1]]^(aux[[i, 2]]-1), {i, L}]]};
moves[n_] :=moves[n] = Module[{aux = FactorInteger[n], L=Length[ FactorInteger [n]]}, Union[Flatten[Table[n/aux[[i, 1]]^j, {i, 1, L}, {j, 1, aux[[i, 2]]}], 1], A003557[n]]]; los[1]=True; los[m_] := los[m] = If[PrimeQ[m], False, Union@Flatten@Table[los[moves[m][[i]]], {i, 1, Length[moves[m]]}] == {False}]; Select[Range[400], los]
CROSSREFS
KEYWORD
nonn
AUTHOR
José María Grau Ribas, Jan 21 2021
STATUS
approved