What does it mean for a positive integer to be a power of a prime?

Question

I have a question that states: "If n is a positive integer, and σ(n) is prime then n is a power of a prime number." In this case σ(n) = the number of positive divisors of n.

What does it mean for a positive integer to be a power of a prime?

Answer 1

It means it is a prime raised to a specific power. Take for example $2$, this number is prime. It is also a prime power as it is $2^1$. Another example of a power of a prime would be $8=2^3$. The number $6$ is not a prime power as $6=2\times 3$ and $2,3$ are distinct primes.

Answer 2

  n : 1 =   1    sigma(n) : 1 =   1 
  n : 2 =  2   sigma(n) : 3 =  3
  n : 4 =  2^2   sigma(n) : 7 =  7
  n : 9 =  3^2   sigma(n) : 13 =  13
  n : 16 =  2^4   sigma(n) : 31 =  31
  n : 25 =  5^2   sigma(n) : 31 =  31
  n : 64 =  2^6   sigma(n) : 127 =  127
  n : 289 =  17^2   sigma(n) : 307 =  307
  n : 729 =  3^6   sigma(n) : 1093 =  1093
  n : 1681 =  41^2   sigma(n) : 1723 =  1723
  n : 2401 =  7^4   sigma(n) : 2801 =  2801
  n : 3481 =  59^2   sigma(n) : 3541 =  3541
  n : 4096 =  2^12   sigma(n) : 8191 =  8191
  n : 5041 =  71^2   sigma(n) : 5113 =  5113
  n : 7921 =  89^2   sigma(n) : 8011 =  8011
  n : 10201 =  101^2   sigma(n) : 10303 =  10303
  n : 15625 =  5^6   sigma(n) : 19531 =  19531
  n : 17161 =  131^2   sigma(n) : 17293 =  17293
  n : 27889 =  167^2   sigma(n) : 28057 =  28057
  n : 28561 =  13^4   sigma(n) : 30941 =  30941
  n : 29929 =  173^2   sigma(n) : 30103 =  30103
  n : 65536 =  2^16   sigma(n) : 131071 =  131071
  n : 83521 =  17^4   sigma(n) : 88741 =  88741
  n : 85849 =  293^2   sigma(n) : 86143 =  86143