How many positive divisors does 2^n have where n is a positive integer

set of divisors={1,2,2^2=4,2^3=8,.....,2^n}
hence= n+1 divisors

One is tempted to say "only one", considering only prime numbers
(the only divisor is 2)

However, if you consider any integer, then all non-negative integer powers of 2 can be integer divisors of 2^n
so that is (n+1) divisors.

2^0 (= 1), 2^1, 2^2, ... 2^(n-2), 2^(n-1), 2^n

n + 1

2^1 = 2 (prime 1 and 2 divisors)
2^2 = 4 (1, 2, 4 divisors)
2^3 = 8 (1, 2, 4, 8 divisors)
etc.