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