%I #25 Apr 16 2022 21:33:01

%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 number-of-divisors function d = A000005, with initial value n.

%C The iterated d function rapidly converges to fixed point 2. In the 5th iterated d-sequence, 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 non-stationary 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 Table[Nest[DivisorSigma[0,#]&,n,5],{n,110}] (* _Harvey P. Dale_, Jun 18 2021 *)

%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_

%E Previous Mathematica program replaced by _Harvey P. Dale_, Jun 18 2021