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)}.

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Mar 10 2003

Keywords

• nonn

Comments

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

A081211(n) = A081213(n) iff a(n) <= 2; a(A131072(n)) > 2. - Reinhard Zumkeller, Jun 13 2007

Links

• R. Zumkeller, Table of n, a(n) for n = 1..10000

Programs

Mathematica

gsf[n_] := For[k = n, True, k--, If[SquareFreeQ[k], Return[k]]];
A081210[n_] := Times @@ gsf /@ Power @@@ FactorInteger[n];
a[n_] := Module[{cnt = 0}, FixedPoint[(cnt++; A081210[#])&, n]; cnt-1];
Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Mar 27 2013, updated Nov 27 2023 *)