Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $41$.

share|improve this question

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 :-)

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.