Answer: 160

Answer: Yes, it is!
Adding up the divisors of 8128: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064 = 8128

Answer: Paul Erdős, of course!
As the Erdős number describes the "collaborative distance" in authorship of mathematical papers between mathematician Paul Erdős and another person it is only natural that Paul Erdős holds this position.

Answer: 91

Answer: 4 trivial factors.
The positive +1 and +N and the negative -1 and -N.

Answer: Leonhard Euler.
Swiss-born Euler is held to be one of the greatest mathematicians in history. He made pioneering contributions to several branches of mathematics and introduced much of the modern mathematical terminology and notation.

Answer: Paul Erdős
Erdős published at least 1,525 mathematical papers during his lifetime. He engaged more than 500 collaborators and devoted most of his time to mathematics up until his death in 1996 at the age of 83 years old.

Answer: 73

Answer: Pierre-Simon Laplace has an Erdős number of at most 14!
According to "The Erdös number project" a path to Laplace was found by Leonid Yanushevich giving the famous mathematician an Erdös number of at most 14.

Answer: A perfect number.
You might also think of a perfect number as a number that is half the sum of all of its positive divisors, including itself! This definition is at least 2300 years old as it appears in Euclid's "Elements".