Is p^n Deficient if p is a Prime?

[imprank6]

Homework Statement

Show that if p is a prime, then p^n is deficient.

Homework Equations

The Attempt at a Solution

I have no idea where to start.

 

[VeeEight]

You could start with the definition of a deficient number.
If p is prime, it's only divisors are 1 and p and thus, the sum of it's divisors is p+1.
What are the divisors of pⁿ?

 

[imprank6]

You could start with the definition of a deficient number.
If p is prime, it's only divisors are 1 and p and thus, the sum of it's divisors is p+1.
What are the divisors of pⁿ?

would be P^n +P^1+P^0 correct?

 

[VeeEight]

If p is prime, then it's only divisors are 1 and p. The divisors of p^{n are also 1 and p, which sum to p+1. Apply this to the criteria of a deficient number.}