Consecutive Prime Powers
Find the sum of all positive integers \(N\) such that \(N-1\), \(N\), and \(N+1\) are all prime powers.
Details and assumptions
A prime power is a positive integer that can be expressed in the form \(p^a\), where \(p\) is a prime and \(a\) is a positive integer.
The question has been updated to standardize the definition of a prime power.