Given $A$ and $B$, how many positive integers $N$ such that $N\times B$ has at least one divisior $D$ that lies in $N \lt D \le A$? 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 $41$.
Are you expecting some simple math formula for the following value?
$$\left|\left\{n\in\mathbb{N}\ :\ \exists n_1,n_2,d\in\mathbb{N}\ :\ n=n_1 n_2,\ \ d\mid B,\ \ n_1&lt;d,\ \ n_2\le\frac Ad\right\}\right|$$
Hard to believe such formula exists.
But it can be computed :-)
Are you expecting some simple math formula for the following value?
$$\left|\left\{n\in\mathbb{N}\ :\ \exists n_1,n_2,d\in\mathbb{N}\ :\ n=n_1 n_2,\ \ d\mid B,\ \ n_1&lt;d,\ \ n_2\le\frac Ad\right\}\right|$$
Hard to believe such formula exists.
But it can be computed :-)