No real requirements except for the one listed in the online documentation at page 1: http://www.lansweeper.com/documentation.pdf
For larger installations of course the requirements become more important.
We recommend installing the services (SQL, Web, Main scan) on virtual machines as this is the most flexible. We do the same. (Regarding Vmware speed: Lansweeper works fastest if you have multiple cores/virtual processors. Memory is not that important. 8 GB RAM should be fine to start with)
In general: We actually do not have specific processor or memory requirements. Lansweeper should run on any hardware purchased in the last 5 years. The more processors, the more memory and the faster your disks, the better. Having multiple processors will speed up scanning a lot. Memory has less of an impact.
A normal dimensioned scanning server can easily scan 5000 assets a day. We advise to install a scanning server in the sites with the most assets if you can afford the Enterprise license. Best practice to install the Lansweeper database in the site that has the most assets (e.g. headquarter) to avoid unnecessary traffic between the sites.
You could install a scanning server in each site and although 40 scanning servers is not exceptional, keep in mind on upgrade you will need to run the installer on each server.
For the SQL Server:
Best to install SQL Server Edition 2008 R2 or 2012 and have the latest patches available installed.
For 4,000 client computers, we expect a final database size of 4GB-20GB, depending on how much information you plan on scanning and how much history you plan on keeping. Devices such as printers and routers take up very little database space.
To optimize your SQL Server we must refer to other sources as this is a profession on its own.
We recommend to back up the database on regular bases, but at least before each upgrade or running risky scripts on the database.
For the server hosting the web console (IIS) the hardware doesn’t matter that much. Most clients scanning from 50 to 5000 assets install all 3 components (SQL, Web, Scanning) on the same machine...