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A036453
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a(n)=d(d(d(d(d(n))))), the 5th iterate of number-of-divisors function with initial value of n.
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9
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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
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OFFSET
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1,2
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COMMENTS
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The iterated d function rapidly converges to fixed point 2. In the 5-th 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. [From R. J. Mathar, Oct 20 2008]
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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EXAMPLE
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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).
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MATHEMATICA
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a[ n ]=Nest[ d, n, 5 ]
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PROG
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(PARI) a(n)=my(d=numdiv); d(d(d(d(d(n))))) \\ Charles R Greathouse IV, Apr 07 2012
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CROSSREFS
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Cf. A000005, A010553, A036450, A036452.
Sequence in context: A046698 A007395 * A040000 A055642 A138902 A211668
Adjacent sequences: A036450 A036451 A036452 * A036454 A036455 A036456
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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STATUS
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approved
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