Answer: 4275

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

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: 5
Portman collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird, who has a collaboration path (Gazzaniga, Michael S. -> Victor, Jonathan D.) leading to Joseph Gillis, who has an Erdős number of 1.

Answer: 312211
John Conway's "look and say" sequence has no digits other than 1, 2, and 3 in it, unless the seed number contains such a digit or a run of more than three of the same digit. A degenerate sequence appears with the seed of 22.

Answer: 91

Answer: 160

Answer: 333

Answer: No, it's not!
Adding up the divisors of 36: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55

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".