An Idea of Mr. A

Mr. A proposes to his son the following problem:

"Consider two integers n_1 and n_2 such that 1 \le n_1 < n_2 \le 10^4.

Using the function p:N^{*}\to N^{*}, p(n)=2^n, n \in N^{*} (where N^{*} is the set of positive integers) we define the set

We also define a set of pairs as follows:

Consider the formula:

where \gcd(m_1,m_2) is the greatest common divisor of m_1 and m_2. The problem asks to find the number R(n_1,n_2)."

Solve the problem proposed by Mr. A.