Yes, correct, you got it. I always say : 's zaterdags. Op zaterdagen has https://www.google.nl/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=op%20zaterdagen Ongeveer 463.000 resultaten while 's zaterdags has ongeveer 330.000 resultaten. So google does not agree with me, but maybe that is because 's zaterdags, is a little bit more informal, it is also shorter than "op zaterdagen".
Dank u wel. That's very helpful!
There's another related question I have left unanswered from another thread as well: if I'm referring to something happening this upcoming Saturday, how would this most naturally be expressed in Dutch?
Zaterdag wil ik gaan. OR Op zaterdag wil ik gaan.
Both sentences (Zaterdag wil ik gaan. OR Op zaterdag wil ik gaan.) are understandable and correct. Although, it sounds a little bit English. .. wil = to want, like to go. Is that really what you mean? "Zaterdag wil ik gaan" is the best. The other sentence would be better if you changed the order of the words: "Ik wil op zaterdag gaan." It is also related to the context. If the question is: Wanneer wil je op vakantie gaan? Then the answer would definitely be: 'Zaterdag wil ik gaan", of "Zaterdag wil ik vertrekken." Vakantie takes a longer time period then just one day. If we are taking about a one day event , like visiting parents. The question could be: Wanneer ga je naar je ouders? "Op zaterdag wil ik gaan" would be better. "Op" is pointing at exactly the Saterday. Putting Zaterdag in front of the sentence gives it more importance. In this sentence Zaterdag is important, not the IK, or gaan.
In English, yes, "on Saturdays" is very similar to "every Saturday" if the sentence is positively phrased:
"She goes every Saturday" = she rarely, if ever, misses a Saturday.
If the sentence is phrased in the negative, though, it's a little different.
"She doesn't go on Saturdays" = she never goes on a Saturday.
"She doesn't go every Saturday" = She goes on some Saturdays, but not all Saturdays.