A225320 The number of iterations of the bi-unitary totient A116550 needed to reach 1 starting with n.

0, 1, 2, 3, 4, 3, 4, 5, 6, 4, 5, 6, 7, 7, 7, 8, 9, 7, 8, 8, 8, 8, 9, 10, 11, 8, 9, 9, 10, 8, 9, 10, 10, 11, 12, 11, 12, 10, 10, 10, 11, 9, 10, 13, 12, 11, 12, 12, 13, 12, 13, 10, 11, 11, 10, 12, 10, 10, 11, 12, 13, 13, 14, 15, 13, 13, 14, 13, 14, 11, 12, 14, 15, 12, 13, 15, 14, 10, 11, 14

Offset: 1

Author

R. J. Mathar, May 05 2013

Keywords

• nonn

Examples

			a(6) = 3 because the first step is A116550(6) = 3, the second A116550(3) = 2, the third A116550(2) = 1, where 1 is reached.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005424 (positions of records), A116550.

Programs

Maple

A225320 := proc(n)
    option remember;
    if n = 1 then
        0;
    else
        1+procname(A116550(n)) ;
    end if;
end proc:

Mathematica

A116550[1] = 1; A116550[n_] := With[{pp = Power @@@ FactorInteger[n]}, Count[Range[n], m_ /; Intersection[pp, Power @@@ FactorInteger[m]] == {}]]; a[n_] := a[n] = If[n == 1, 0, 1 + a[A116550[n]]]; Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Dec 16 2013 *)

Formula

The smallest x such that A116550^x(n) = 1, where the operation Op^x denotes x nestings of the operator Op.