A340780 Losing positions n (P-positions) in the following game: two players take turns dividing the current value of n by either a prime power > 1 or by A007947(n) to obtain the new value of n. The winner is the player whose division results in 1.
1, 12, 18, 20, 28, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99, 116, 117, 120, 124, 147, 148, 153, 164, 168, 171, 172, 175, 188, 207, 212, 216, 236, 242, 244, 245, 261, 264, 268, 270, 275, 279, 280, 284, 292, 312, 316, 325, 332, 333, 338, 356, 363, 369, 378, 387, 388
Offset: 1
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Programs
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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]
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