Yes, you can use same mobile number to register on multiple devices. Your profile along with downloaded songs, purchased songs, liked songs, playlists and subscription will synchronise across devices.

But you will still have to re-download songs in memory.

Steps to re-download downloaded songs are mentioned below:

Step 1: Launch Wynk Music

Step 2: Go to My Music

Step 3: Go to All Downloaded

Step 4: Tap on 'Download All' button

Steps to re-download purchased songs are mentioned below:

Step 1: Launch Wynk Music

Step 2: Go to My Music

Step 3: Go to All Purchased

Step 4: Tap on 'Download All' button

Please note that downloading all songs may take time depending on number of songs to download and network conditions.