A081212 - OEIS

%I #17 Nov 27 2023 07:43:23

%S 0,0,0,1,0,0,0,1,1,0,0,2,0,0,0,1,0,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,

%T 0,1,0,0,0,1,0,0,0,1,1,0,0,2,1,1,0,1,0,2,0,2,0,0,0,2,0,0,2,1,0,0,0,1,

%U 0,0,0,2,0,0,1,1,0,0,0,2,1,0,0,3,0,0,0,1,0,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0

%N Let r(n,k) = if k=0 then n else r(A081210(n),k-1), then a(n) = Min{i:r(n,i) = r(n,i+1)}.

%C Number of times A081210 is to be applied to n until a fixed-point is reached, A081213(n)=r(n,a(n)).

%C A081211(n) = A081213(n) iff a(n) <= 2; a(A131072(n)) > 2. - _Reinhard Zumkeller_, Jun 13 2007

%H R. Zumkeller, <a href="/A081212/b081212.txt">Table of n, a(n) for n = 1..10000</a>

%t gsf[n_] := For[k = n, True, k--, If[SquareFreeQ[k], Return[k]]];

%t A081210[n_] := Times @@ gsf /@ Power @@@ FactorInteger[n];

%t a[n_] := Module[{cnt = 0}, FixedPoint[(cnt++; A081210[#])&, n]; cnt-1];

%t Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Mar 27 2013, updated Nov 27 2023 *)

%K nonn

%O 1,12

%A _Reinhard Zumkeller_, Mar 10 2003