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A081212 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)}.

%I A081212 #17 Nov 27 2023 07:43:23
%S A081212 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 A081212 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 A081212 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 A081212 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 A081212 Number of times A081210 is to be applied to n until a fixed-point is reached, A081213(n)=r(n,a(n)).
%C A081212 A081211(n) = A081213(n) iff a(n) <= 2; a(A131072(n)) > 2. - _Reinhard Zumkeller_, Jun 13 2007
%H A081212 R. Zumkeller, <a href="/A081212/b081212.txt">Table of n, a(n) for n = 1..10000</a>
%t A081212 gsf[n_] := For[k = n, True, k--, If[SquareFreeQ[k], Return[k]]];
%t A081212 A081210[n_] := Times @@ gsf /@ Power @@@ FactorInteger[n];
%t A081212 a[n_] := Module[{cnt = 0}, FixedPoint[(cnt++; A081210[#])&, n]; cnt-1];
%t A081212 Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Mar 27 2013, updated Nov 27 2023 *)
%K A081212 nonn
%O A081212 1,12
%A A081212 _Reinhard Zumkeller_, Mar 10 2003