A049865 Number of iterations of unitary totient function (A047994) required to reach 1 from n.

0, 1, 2, 3, 4, 2, 3, 4, 5, 4, 5, 3, 4, 3, 5, 6, 7, 5, 6, 4, 4, 5, 6, 4, 5, 4, 5, 6, 7, 5, 6, 7, 5, 7, 5, 5, 6, 6, 5, 7, 8, 4, 5, 6, 8, 6, 7, 6, 7, 5, 8, 6, 7, 5, 8, 5, 6, 7, 8, 5, 6, 6, 7, 8, 7, 5, 6, 7, 7, 5, 6, 6, 7, 6, 7, 6, 6, 5, 6, 6, 7, 8, 9, 6, 9, 5, 6, 6, 7, 8, 7, 6, 6, 7, 7, 7, 8, 7, 7, 7, 8, 8, 9, 7, 7, 7, 8, 6, 7, 8, 7

Offset

1,3

Comments

a(A003271(n)) = n and a(m) <> n for m < A003271(n). [Reinhard Zumkeller, Aug 17 2011]

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Maple

A049865 := proc(n)
    if n = 1 then
        0 ;
    else
        1+procname( A047994(n)) ;
    end if;
end proc: # R. J. Mathar, May 02 2013

Mathematica

uphi[n_] := (f = FactorInteger[n]; Times @@ (f[[All, 1]]^f[[All, 2]] - 1)); uphi[n_ /; n <= 1] = 1; a[n_] := (k = 0; FixedPoint[ (k++; uphi[#]) & , n]; k-1); Table[a[n], {n, 1, 120}] (* Jean-François Alcover, Jan 20 2012 *)

Prog

(Haskell)
a049865 n = length $ takeWhile (> 1) $ iterate a047994 n
a049865_list = map a049865 [1..]
-- Reinhard Zumkeller, Aug 17 2011

Crossrefs

Sequence in context: A151925 A106653 A173524 * A070771 A274640 A245341

Adjacent sequences: A049862 A049863 A049864 * A049866 A049867 A049868

Keyword

nonn,easy,nice

Author

David W. Wilson

Status

approved