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.

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