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

1,3

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A005424 (positions of records), A116550.

Sequence in context: A125619 A349946 A262519 * A308937 A123066 A330239

Adjacent sequences: A225317 A225318 A225319 * A225321 A225322 A225323

Keyword

nonn

Author

R. J. Mathar, May 05 2013

Status

approved