APP icons for android and IOS

good morning,
I have to produce the set of icons to represent an app on different platforms and contexts.
I am able to produce images at different resolutions but having no previous experience in producing icons for Android and IOS APPs, so I would like help.

From what I understand from the request I received, each size corresponds to a specific requirement requested by the Apple App Store and Google Play Store.

Required sizes for Android and iOS:

72x72, 48x48, 96x96, 144x144, 192x192
if I understood correctly, these resolutions are mainly used for Android on devices with various pixel densities (mdpi, hdpi, xhdpi, xxhdpi, xxxhdpi).

20x20, 29x29, 40x40, 60x60, 76x76
if I understand correctly, these resolutions are mainly used for iOS in contexts such as notifications, spotlight and main icon, with multipliers (1x, 2x, 3x) indicating Retina densities.

167x167: required size for icons on iPad devices.

I have the logo for the APP in vector format, so I can produce quality output with illustrator.
however it is not clear to me which format to provide (jpg, png, ...) nor if it is appropriate to have special precautions before output.

thanks for the help.