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A036459
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Number of iterations required to reach stationary value when repeatedly applying d, the number of divisors function (A000005).
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10
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0, 0, 1, 2, 1, 3, 1, 3, 2, 3, 1, 4, 1, 3, 3, 2, 1, 4, 1, 4, 3, 3, 1, 4, 2, 3, 3, 4, 1, 4, 1, 4, 3, 3, 3, 3, 1, 3, 3, 4, 1, 4, 1, 4, 4, 3, 1, 4, 2, 4, 3, 4, 1, 4, 3, 4, 3, 3, 1, 5, 1, 3, 4, 2, 3, 4, 1, 4, 3, 4, 1, 5, 1, 3, 4, 4, 3, 4, 1, 4, 2, 3, 1, 5, 3, 3, 3, 4, 1, 5, 3, 4, 3, 3, 3, 5, 1, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Iterating d for n, the prestationary prime and finally the fixed value of 2 is reached in different number of steps; a[ n ] is the number of required iterations.
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FORMULA
| a(n) = a(d(n)) + 1. A036459(n) = 1 iff n is an odd prime.
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EXAMPLE
| If n=8, then d[ 8 ]=4, d[ d[ 8 ] ]=3, d[ d[ d[ 8 ] ] ]=2, which means that a[ n ]=3. In terms of number of steps to converge the distance of n from the d-equilibrium is expressed by a[ n ]. Similar method is used in A018194.
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MATHEMATICA
| Table[ Length[ FixedPointList[ DivisorSigma[0, # ] &, n]] - 2, {n, 105}] (from Robert G. Wilson v Mar 11 2005)
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PROG
| (PARI) for(x = 1, 150, for(a=0, 15, if(a==0, d=x, if(d<3, print(a-1), d=numdiv(d) )) ))
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CROSSREFS
| Equals A060937 - 1. Cf. A007624, A036450, A046452, A036453, A036455, A030630.
Sequence in context: A083868 A128199 A191350 * A079167 A199570 A032741
Adjacent sequences: A036456 A036457 A036458 * A036460 A036461 A036462
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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