Definition:Prime Exponent Function

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

Let the Prime Decomposition of $$n$$ be given as:
 * $$n = \prod_{j=1}^k \left({p \left({j}\right)}\right)^{a_j}$$

where $$p \left({j}\right)$$ is the prime enumeration function.

Then the exponent $$a_j$$ of $$p \left({j}\right)$$ in $$n$$ is denoted $$\left({n}\right)_j$$.

If $$p \left({j}\right)$$ does not divide $$n$$, then $$\left({n}\right)_j = 0$$.

We also define:
 * $$\forall n \in \N: \left({n}\right)_0 = 0$$;
 * $$\forall j \in \N: \left({0}\right)_j = 0$$;
 * $$\forall j \in \N: \left({1}\right)_j = 0$$.