Distribution and upper bound of mimic numbers
Let the notation denote '' divides ''. The mimic function in number theory is defined as follows .
By using this definition of mimic function, the mimic number of any non-prime integer is defined as follows .
Given these two definitions and a positive integer , find the distribution of mimic numbers of those numbers divisible by .
Again, find whether there is an upper bound of mimic numbers for a set of numbers divisible by any fixed positive integer .
* Malay Bhattacharyya, Sanghamitra Bandyopadhyay and U Maulik, Non-primes are recursively divisible, Acta Universitatis Apulensis 19 (2009).
* indicates original appearance(s) of problem.