Definition:Sequence Coding

Definition
Let $\left \langle {a_1, a_2, \ldots, a_k}\right \rangle$ be a finite sequence in $\N^*$ (that is, $\forall i \in \left\{{1, 2, \ldots, k}\right\}: a_i > 0$).

Let $p_i$ be the $i$th prime number, so that: etc.
 * $p_1 = 2$
 * $p_2 = 3$
 * $p_3 = 5$
 * $p_4 = 7$

Let $n = p_1^{a_1} p_2^{a_2} \cdots p_k^{a_k}$ where $p_i$ is the $i$th prime number.

Then $n \in \N$ codes the sequence $\left \langle {a_1, a_2, \ldots, a_k}\right \rangle$, or $n$ is the code number for the sequence $\left \langle {a_1, a_2, \ldots, a_k}\right \rangle$.

The set of all code numbers of finite sequences in $\N$ is denoted $\operatorname{Seq}$.

Note that $n \in \operatorname{Seq}$ iff $n$ is divisible by all the primes $p_1, p_2, \ldots, p_k$, where $p_k$ is the largest prime dividing $n$.