STATUS
proposed
approved
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a(n) = d(d(d(d(d(n))))), the 5th iterate of the number-of-divisors function d = A000005, with initial value n.
(history; published version)
(history; published version)
STATUS
editing
proposed
NAME
a(n) = d(d(d(d(d(n))))), the 5th iterate of the number-of-divisors function d = A000005, with initial value n.
COMMENTS
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.
Differs from A007395 for n = 1, 5040, 7920, 8400, 9360, 10080, 10800 , etc. - R. J. Mathar, Oct 20 2008
EXAMPLE
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).
STATUS
approved
editing
STATUS
editing
approved
MATHEMATICA
a[ n ]=Nest[ d, n, 5 ]
Table[Nest[DivisorSigma[0, #]&, n, 5], {n, 110}] (* Harvey P. Dale, Jun 18 2021 *)
EXTENSIONS
Previous Mathematica program replaced by Harvey P. Dale, Jun 18 2021
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
NAME
a(n) = d(d(d(d(d(n))))), the 5th iterate of the number-of-divisors function with initial value of n.
COMMENTS
Differs from A007395 for n=1, 5040, 7920, 8400, 9360, 10080, 10800 etc. [From _- _R. J. Mathar_, Oct 20 2008]
EXAMPLE
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).
STATUS
approved
editing