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

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, 26, 21, 29, 30, 31, 31, 33, 34, 35, 21, 37, 38, 39, 35, 41, 42, 43, 33, 35, 46, 47, 35, 47, 46, 51, 39, 53, 39, 55, 47, 57, 58, 59, 35, 61, 62, 47, 62, 65, 66, 67, 51, 69, 70, 71, 47, 73

Offset: 1

Author

Reinhard Zumkeller, Mar 10 2003

Keywords

• nonn

Comments

A081210(a(n)) = a(n).

Different from A081211.

a(n) = A081211(n) for n<84 = A131072(1); a(A131072(n)) <> A081211(A131072(n)). - Reinhard Zumkeller, Jun 13 2007

Links

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

Crossrefs

Cf. A081210, A081211, A081212, A081214.

Cf. A131072.

Programs

Maple

A081212r := proc(n,k)
    option remember ;
    if k =0 then
        n;
    else
        procname(A081210(n),k-1) ;
    end if;
end proc:
A081212 := proc(n)
    local i ;
    for i from 0 do
        if A081212r(n,i) = A081212r(n,i+1) then
            return i ;
        end if;
    end do:
end proc:
A081213 := proc(n)
    A081212r(n,A081212(n)) ;
end proc:
seq(A081213(n),n=1..84) ; # R. J. Mathar, May 25 2023

Mathematica

gsf[n_] := For[k = n, True, k--, If[SquareFreeQ[k], Return[k]]];
A081210[n_] := (cnt++; Times @@ gsf /@ Power @@@ FactorInteger[n]);
A081212[n_] := (cnt = 0; FixedPoint[A081210, n]; cnt - 1);
r[n_, k_] := r[n, k] = If[k == 0, n, r[A081210[n], k - 1]];
a[n_] := r[n, A081212[n]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Sep 12 2023 *)