The one I've been using for years and years is A Soft Murmur [0]. You can put together a mix of a few sounds to suit your preference. I like to prioritize the coffee shop and rain (about 50% each) with some thunder (25%) and a light fire (25%). There's also a "meander" option where any non-silenced sound's volume will move up and down at random so it's not the exact same sounds for the whole time.
I dunno how you can be productive in perfect silence. If I have perfect silence I find myself getting anxious and distracted. I work best when I can hear other people around me being productive in some way.
Sometimes I need a little bit of noise to help with focus, and sometimes I just put on jazz anyways.
I have been toying with an idea for a few years of doing something just like that. But with arcade sounds. But ideas are just ideas :)...
edit this exact page I think i've found 3x now; and then lost it in this way.