Hi Tom,
this all depends on the workload you are planning to introduce to your ESXi servers. Even then the answer needs to be refined further - will you need to cluster the ESXi hosts in order to have application dependency? (e.g. SQL Cluster & Generic Cluster). You will also need one or two ESXi hosts more in order to satisfy HA Failover so that your failed VMs can reboot on a host with enough capacity (governed by DRS).
So it all boils down how used are the application servers during peak times (business hours), how much frequency and vCPU they need, and if you can combine them with servers like DNS, AD, and further lightweight services. You need to talk to your app owners in terms of what they requires.
Sizing an ESXi host for 4000vCores would mean you should be able to put 400VMs on a cluster. This large scale seems it would be used for VDI?
Stop by my blog if you'd like 🙂 I dabble in vSphere troubleshooting, PowerCLI scripting and NetApp storage - and I share my journeys at http://vmxp.wordpress.com/