"Computer admin" vs active account?
The best way to solve this is to have one user who is an Admin and has a password.

In System Preferences navigate to Users &amp; Groups. 


Ensure you only have one active user.
Ensure that user has a password.



  Note: You might need to click the Lock button to make changes.




Then click Back in System Preferences. Navigate to Security &amp; Privacy. Click the Lock button to make changes. Uncheck all three checkboxes:



Now you will be able to turn on the computer without logging in. OS X will launch directly to the desktop. If you need to perform a Administrator level operation like using sudo in Terminal, you will be prompted for the password. Magic! :)