If the goal is to save the file locally for opening in your favorite PDF reader, I wouldn't even activate a link for same because, as Sieghard has noted, under Chrome that generally opens the file in Chrome's built-in PDF viewer in a separate tab, and then you still have to get to the download button.
Just bring up the context menu when you have focus on the actual link to the PDF file and choose, "Save link target as" (or similar, I can never remember if that's the Firefox language or Chrome's, but they're similar enough that it's pretty obvious).
Brian - Windows 10 Pro, 64-Bit, Version 1809, Build 17763
Here is a test to find out whether your mission in life is complete. If you’re alive, it isn’t.
~ Lauren Bacall