There are two ways cores on a physical machine affect ArcGIS Server.
1. Licensing - Every license of ArcGIS Server is for 4 CPU cores.
2. Performance - The System Design Strategy guide states that peak throughput for ArcGIS Server is reached if total map services instances are 3 - 5 (average 4) per core. Therefore, on a 4 core machine you could get peak throughput by configuring a total 16 map services instances.*
Many computers today have a hyper-threaded CPU which show more number of logical processors than cores. See image below.
On such machines, is ArcGIS Server licensing and performance to consider this as a 4 core or a 8 core machine?
For licensing - should I purchase two licenses?
For performance - can I configure 16 or 32* map service instances?
*4 map service instances per core may not always be the case and this number may change as per you service contents and configuration. For more details, refer to the Server Software Performance section of the System Design Strategy guide.