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
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
B. L. Mayer and L. H. A. Monteiro, On the divisors of natural and happy numbers: a study based on entropy and graphs, AIMS Mathematics (2023) Vol. 8, Issue 6, 13411-13424.
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 d-equilibrium 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(a-1), d=numdiv(d) )) ))
(PARI) a(n)=my(t); while(n>2, n=numdiv(n); t++); t \\ Charles R Greathouse IV, Apr 07 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved