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A036450
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a(n)=d[ d[ d[ n ] ] ], the 3rd iterate of number-of-divisors function with initial value of n.
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13
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1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2, 4, 2, 3, 2, 2, 2, 4, 2, 3, 3, 2, 2, 3, 2, 3, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The iterated d function rapidly converges to the fixed point 2.
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LINKS
| Enrique Pérez Herrero, Table of n, a(n) for n = 1..2000
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FORMULA
| a[ n ]=Nest[ d, n, 3 ]
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EXAMPLE
| E.g. n=5040,d[ 5040 ]=60,d[ d[ 5040 ] ]=d[ 60 ]=12 and a[ 5040 ]=d[ 12 ]=6
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MATHEMATICA
| f[n_]:=Length[Divisors[n]]; Table[Nest[f, n, 3], {n, 6!}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 10 2010]
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CROSSREFS
| Cf. A000005, A010553, A036452, A036453.
Sequence in context: A111895 A103379 A032550 * A085576 A108622 A112348
Adjacent sequences: A036447 A036448 A036449 * A036451 A036452 A036453
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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