Average of Euler phi function and mobius function and probability two numbers are coprime

Average of Euler phi function and Mobius function and probability two numbers are coprime

Advanced mathematics list:

Analytic number theory:
https://www.youtube.com/playlist?list=PLg9w7tItBlZu2IdPFQkrvAsPs-V2B_dxk

Real analysis:
https://www.youtube.com/playlist?list=PLg9w7tItBlZsaSW0zlQ7m0S3Ti51bYJg_

Group representation for finite group
https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9-

exact sequences
https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9

Ring theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u

group theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v

Category theory
https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi

Field theory in abstract algebra
https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-

Mathematical analysis
https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh