No. The apps are associated with the account used to purchase them. So if you purchased several apps and then switched phones, when you signed into that new phone with the same google account, you will have those apps available to download again onto your new handset. This would apply even if you switched carriers or changed phone numbers. They are strictly account specific and tied to your google login.
Yeah they don't follow phone# they follow Gmail and only the paid apps. So you can change your phone# just not your Gmail.
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