Need some help creating a complex query/aggregation

I'm trying to create a query to help create a retention cohort.
Essentially, my index consists of many records with the fields username,timestamp,taskCompleted
From this data I'm trying to group users into weeks (based on their timestamp) where taskCompleted=registration (essentially grouping users by registration week), and for all users that registered in a given week, I want to bucket all their activity by weeks.

For example, if I have 100 users total, 10 of which registered on week X. For those 10 users, I want to bucket all their activity into a week by week basis, which I then plan to apply cardinality on. I then want this to happen not just for registrations on week X, but weeks X-Z.

If this is still confusing, a retention cohort is splitting users by week of registration, and for every time period (which is a week), how many users had an activity processed.

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