A176839 The number of iterations to reach 1 under the map x -> x-tau(phi(x)), starting at n.

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

Offset

1,4

Comments

Tau(n) = A000005(n) is the number of divisors of n, and phi(n) = A000010(n) is the Euler totient function.

Links

Table of n, a(n) for n=1..85.

Example

a(12)=4 because
f(12) = 12 - tau(phi(12)) = 12 - tau(4) = 12 - 3 = 9;
f(9) = 9 - tau(phi(9)) = 9 - tau(6) = 9 - 4 = 5;
f(5) = 5 - tau(phi(5)) = 5 - tau(4) = 5 - 3 = 2;
f(2) = 2 - tau(phi(2)) = 2 - tau(1) = 2 - 1 = 1, and a(12) = 4.

Maple

A062821 := proc(n)
        numtheory[tau](numtheory[phi](n)) ;
end proc:
A176839 := proc(n)
        a := 0 ;
        x := n ;
        while x <> 1 do
                x := x-A062821(x) ;
                a := a+1 ;
        end do:
        a ;
end proc: # R. J. Mathar, Oct 11 2011

Mathematica

f[n_] := If[n == 1, 1, n - DivisorSigma[0, EulerPhi[n]]];
a[n_] := Length[FixedPointList[f, n]] - 2;
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Apr 09 2024 *)

Crossrefs

Cf. A062821.

Sequence in context: A100678 A026834 A071335 * A179844 A076223 A076235

Adjacent sequences: A176836 A176837 A176838 * A176840 A176841 A176842

Keyword

nonn

Author

Michel Lagneau, Apr 27 2010

Status

approved