

A036459


Number of iterations required to reach stationary value when repeatedly applying d, the number of divisors function (A000005).


25



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
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OFFSET

1,4


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.
Each value n > 0 occurs an infinite number of times. For positions of first occurrences of n, see A251483.  Ivan Neretin, Mar 29 2015


LINKS



FORMULA

a(n) = a(d(n)) + 1 if n > 2.
a(n) = 1 iff n is an odd prime.


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 the number of steps required for convergence, the distance of n from the dequilibrium is expressed by a(n). A similar method is used in A018194.


MATHEMATICA

Table[ Length[ FixedPointList[ DivisorSigma[0, # ] &, n]]  2, {n, 105}] (* Robert G. Wilson v, Mar 11 2005 *)


PROG

(PARI) for(x = 1, 150, for(a=0, 15, if(a==0, d=x, if(d<3, print(a1), d=numdiv(d) )) ))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



