All Questions

I am trying to find an estimate for the following sum: $$ \sum_{\substack{n \leq x \\ n \equiv k (m)}} d(n), $$ where $d(n)$ is number of divisors of $n$. I found estimates for the case when $k$ and ...

Divisor function $d(n,m)$ counts the number of $q\in\Bbb N$ with $b<q<m$ such that $n\bmod q\equiv0$. Given $b>0$ what is the correct asymptotic, probabilistic and average case behavior of ...

Given $n$, what is the largest set of consecutive integers in $[n,2n]$ can we have so that each integer is divisible by a distinct element from $[\log n,2\log n]$ (no partiular order)? So apriori I am ...