# Count The Divisors

There is a certain number $$N = n_1\cdot n_2\cdot n_3\cdots n_k$$, where $$1 \leq n_i \leq 100$$ $$(1\le i \le k)$$ are all distinct positive integers.

We are told the following:

• $$N$$ has $$d$$ (positive) divisors and $$d$$ is odd.
• $$128\cdot N$$ has $$\frac{18}{11}d$$ divisors.
• $$175\cdot N$$ has $$\frac 8 5 d$$ divisors.
• $$213\cdot N$$ has $$\frac 8 3 d$$ divisors.

If $$2016\cdot N$$ has $$\frac A B d$$ divisors, with $$A$$ and $$B$$ coprime positive integers, submit $$A + B$$.

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