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A081213 Let r(n,k) = if k=0 then n, else r(A081210(n),k-1), then a(n)=r(n, A081212(n)).

%I A081213 #17 Sep 12 2023 12:25:25
%S A081213 1,2,3,3,5,6,7,7,7,10,11,7,13,14,15,15,17,14,19,15,21,22,23,21,23,26,
%T A081213 26,21,29,30,31,31,33,34,35,21,37,38,39,35,41,42,43,33,35,46,47,35,47,
%U A081213 46,51,39,53,39,55,47,57,58,59,35,61,62,47,62,65,66,67,51,69,70,71,47,73
%N A081213 Let r(n,k) = if k=0 then n, else r(A081210(n),k-1), then a(n)=r(n, A081212(n)).
%C A081213 A081210(a(n)) = a(n).
%C A081213 Different from A081211.
%C A081213 a(n) = A081211(n) for n<84 = A131072(1); a(A131072(n)) <> A081211(A131072(n)). - _Reinhard Zumkeller_, Jun 13 2007
%H A081213 R. Zumkeller, <a href="/A081213/b081213.txt">Table of n, a(n) for n = 1..10000</a>
%p A081213 A081212r := proc(n,k)
%p A081213     option remember ;
%p A081213     if k =0 then
%p A081213         n;
%p A081213     else
%p A081213         procname(A081210(n),k-1) ;
%p A081213     end if;
%p A081213 end proc:
%p A081213 A081212 := proc(n)
%p A081213     local i ;
%p A081213     for i from 0 do
%p A081213         if A081212r(n,i) = A081212r(n,i+1) then
%p A081213             return i ;
%p A081213         end if;
%p A081213     end do:
%p A081213 end proc:
%p A081213 A081213 := proc(n)
%p A081213     A081212r(n,A081212(n)) ;
%p A081213 end proc:
%p A081213 seq(A081213(n),n=1..84) ; # _R. J. Mathar_, May 25 2023
%t A081213 gsf[n_] := For[k = n, True, k--, If[SquareFreeQ[k], Return[k]]];
%t A081213 A081210[n_] := (cnt++; Times @@ gsf /@ Power @@@ FactorInteger[n]);
%t A081213 A081212[n_] := (cnt = 0; FixedPoint[A081210, n]; cnt - 1);
%t A081213 r[n_, k_] := r[n, k] = If[k == 0, n, r[A081210[n], k - 1]];
%t A081213 a[n_] := r[n, A081212[n]];
%t A081213 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Sep 12 2023 *)
%Y A081213 Cf. A081210, A081211, A081212, A081214.
%Y A081213 Cf. A131072.
%K A081213 nonn
%O A081213 1,2
%A A081213 _Reinhard Zumkeller_, Mar 10 2003