Distribution and upper bound of mimic numbers

facility_cttb@indiatimes.com — Sat, 20 Jun 2009 10:50:40 +0200

Author(s): Bhattacharyya

Problem

Let the notation denote '' divides ''. The mimic function in number theory is defined as follows [1].

Definition For any positive integer divisible by , the mimic function, , is given by,

By using this definition of mimic function, the mimic number of any non-prime integer is defined as follows [1].

Definition The number is defined to be the mimic number of any positive integer , with respect to , for the minimum value of which .

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 .

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