%I
%S 1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N a(n) = d(d(d(d(d(n))))), the 5th iterate of the numberofdivisors function with initial value n.
%C The iterated d function rapidly converges to fixed point 2. In the 5th iterated dsequence the first term different from the fixed point 2 appears at n=5040. The 6th and further iterated sequences have very long initial segment of 2's. In the 6th one the first nonstationary term is a(293318625600)=3. In such sequences any large value occurs infinite many times and constructible.
%C Differs from A007395 for n=1, 5040, 7920, 8400, 9360, 10080, 10800 etc.  _R. J. Mathar_, Oct 20 2008
%H Charles R Greathouse IV, <a href="/A036453/b036453.txt">Table of n, a(n) for n = 1..10000</a>
%e E.g., n=96 and its successive iterates are 12,6,4,3 and 2. The 5th term is a(96)=2 is stationary(fixed).
%t a[ n ]=Nest[ d, n, 5 ]
%o (PARI) a(n)=my(d=numdiv);d(d(d(d(d(n))))) \\ _Charles R Greathouse IV_, Apr 07 2012
%Y Cf. A000005, A010553, A036450, A036452.
%K nonn
%O 1,2
%A _Labos Elemer_
