A036453 a(n) = d(d(d(d(d(n))))), the 5th iterate of the number-of-divisors function d = A000005, with initial value n.

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, 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, 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

Offset

1,2

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

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).

Mathematica

Table[Nest[DivisorSigma[0, #]&, n, 5], {n, 110}] (* Harvey P. Dale, Jun 18 2021 *)

Prog

(PARI) a(n)=my(d=numdiv); d(d(d(d(d(n))))) \\ Charles R Greathouse IV, Apr 07 2012

Crossrefs

Cf. A000005, A010553, A036450, A036452.

Sequence in context: A046698 A211662 A007395 * A040000 A211665 A239374

Adjacent sequences: A036450 A036451 A036452 * A036454 A036455 A036456

Keyword

nonn

Author

Labos Elemer

Extensions

Previous Mathematica program replaced by Harvey P. Dale, Jun 18 2021

Status

approved