In this case, you don't use the after the of because
number of students
makes one phrase.
Logically speaking nothing really wrong with "the number of the students," but it's unnecessary because you can take "number of students" as a phrase, and the sentence flows better without the extra the. The concern of interpretation as nominal number is, I believe, matter of the context.
Here is another example:
~ due to a delay in (the) approval
I was once corrected it to without 'the.' But according to Ngram, both with or without the is used:
It took me a while how it works without the here when the approval is about the topic of (the) discussion (here, too, you definitely prefer without the in front of discussion).
I came to this conclusion that it works without the when it can be taken as a phrase (, though it's difficult for non-native speakers like me to know when it's taken as a phrase ).