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A036453 a(n) = d(d(d(d(d(n))))), the 5th iterate of the number-of-divisors function with initial value n. 9
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 (list; graph; refs; listen; history; text; internal format)
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

a[ n ]=Nest[ d, n, 5 ]

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: A130130 A046698 A007395 * A040000 A239374 A262190

Adjacent sequences:  A036450 A036451 A036452 * A036454 A036455 A036456

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)