Form of Divisors of Proth numbers

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Proth number is a number of the form :

$z⋅2^k+1$ where z is an odd positive integer and k is a positive integer such that : $2^k>z$

Is there a form for divisors of Proth Numbers? (Like Mersenne and Fermat Numbers have specific forms of divisors) My search did not turn any results.

Thank you...

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After a long search I came to the same conclusion. There is No such form.