Hi @Alfred W,
Welcome to the Microsoft Q&A forum.
I understand that you are trying to sign in to Outlook on an iOS device. However, even though you have opened the Authenticator app, you are not receiving any notification to approve the sign-in request.
I see that you have tagged this post with Education, so I will provide information based on an Education account.
First, please try restarting your iOS device to check whether the issue is resolved.
If the issue persists, you will not be able to resolve this on your own. Instead, you need to contact your school’s administration team (such as the IT department or administrative office) and ask them to reset MFA for your account.
After MFA has been reset, the next time you sign in, you will be prompted to set up MFA again, and the issue should be resolved.
I hope this information is helpful.
If you have any questions or need further assistance, please feel free to share them in the comments on this post so I can continue to support you.
I look forward to continuing the conversation.
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