It is stated in https://oeis.org/A064078 that Zsigmondy numbers, Z, are the maximal overpseudoprimes base 2 that divide $2^n-1$, where n is the multiplicative order of 2 modulo Z ($2^n-1\equiv 0\mod Z$).
However, I could not find a proof of this online. Zsigmondy numbers can also be thought of as the product of all of the primitive prime divisors of $2^n-1$ as they are coprime to all the previous terms. My questions are:
(1)What is a proof that they are the overpseudoprimes? (2)Are there any other properties of Zsigmondy numbers? (3)Additionally, is this generalizable for base k?
Any answers would be much appreciated as I cannot find many resources online.