Script to login to several servers and get files

Hi ppl,
I am looking out for a shell script
a. That would have to login(from a main server) to say 16 servers individually.
b.On each server go to a particular location, check if a particular file is generated on a date(say every sunday it gets generated and i would be interested in the latest one),
c.if the latest file is present, retrieve the file to main server.
d.if the latest file is not present, wait and check later.
e. This has to be repeated until the files from all 16 servers reach the main server.

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