ABSTRACT.
The results of this talk are elementary. It can be seen that various values can be obtained by iterating the restricted divisor functions. If we consider iteration of t-free divisor functions, then the values of them sees four cases, that is, stable, amicable pair, sociable, unpredictable sequence. Based on the results calculated with Mathematica 12.3, problems with statble numbers and the simplest case of t=2 are introduced. Finally, we introduce problems related to Mersenne primes. Most of this talk is in https://doi.org/10.1002/mma.7555