7/29/17 Hot 100: Every AT40 debut is also a Hot 100 debut

[80sat40fan]

I am not much of a Top 40 music follower these days (I'm more into adult alternative) so if this chart feat occurs frequently, I apologize. In checking out the 7/29/17 Hot 100, I noticed that there are four debut songs. All four songs also debut on the Hot 100 this week. Has it ever happened that every AT40 debut was also a Hot 100 debut? Or, has there been a week where there have been five or more AT40 debuts which were also Hot 100 debuts?

The 7/29/17 AT40 debuts are:
* "The Story of O.J." by Jay-Z at #23
* "Praying" by Kesha at #25
* "Bank Account" by 21 Savage at #33
* "4:44", also by Jay-Z, at #35