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

Author

David W. Wilson

Keywords

• nonn
• easy
• nice

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

Programs

Haskell

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

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 *)