Definition:Prime Exponent Function

Definition
Let $n \in \N$ be a natural number.

Let the prime decomposition of $n$ be given as:
 * $\ds n = \prod_{j \mathop = 1}^k \paren {\map p j}^{a_j}$

where $\map p j$ is the prime enumeration function.

Then the exponent $a_j$ of $\map p j$ in $n$ is denoted $\paren n_j$.

If $\map p j$ does not divide $n$, then $\paren n_j = 0$.

We also define:
 * $\forall n \in \N: \paren n_0 = 0$
 * $\forall j \in \N: \paren 0_j = 0$
 * $\forall j \in \N: \paren 1_j = 0$