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For two integers $A$ and $B$, how can we find the number of positive integers $N$ such that $N\times B$ has at least one divisior $D$ that lies in $N \lt D \le A$?

For example, if $A = 100$ and $B = 11$ then the answer is $41$.

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1 Answer 1

Are you expecting some simple math formula for the following value?
$$\left|\left\{n\in\mathbb{N}\ :\ \exists n_1,n_2,d\in\mathbb{N}\ :\ n=n_1 n_2,\ \ d\mid B,\ \ n_1<d,\ \ n_2\le\frac Ad\right\}\right|$$ Hard to believe such formula exists.
But it can be computed :-)

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