## The fundamental theorem of arithmetic is encoded by the von Mangoldt function

Mathematica 8
 A = Table[ Table[If[Mod[n, k] == 0, Exp[MangoldtLambda[n/k]], ""], {k, 1, 12}], {n, 1, 12}]; MatrixForm[A] 

$\left( \begin{array}{cccccccccccc} 1 & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ 2 & 1 & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ 3 & \text{} & 1 & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ 2 & 2 & \text{} & 1 & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ 5 & \text{} & \text{} & \text{} & 1 & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ 1 & 3 & 2 & \text{} & \text{} & 1 & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ 7 & \text{} & \text{} & \text{} & \text{} & \text{} & 1 & \text{} & \text{} & \text{} & \text{} & \text{} \\ 2 & 2 & \text{} & 2 & \text{} & \text{} & \text{} & 1 & \text{} & \text{} & \text{} & \text{} \\ 3 & \text{} & 3 & \text{} & \text{} & \text{} & \text{} & \text{} & 1 & \text{} & \text{} & \text{} \\ 1 & 5 & \text{} & \text{} & 2 & \text{} & \text{} & \text{} & \text{} & 1 & \text{} & \text{} \\ 11 & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & 1 & \text{} \\ 1 & 1 & 2 & 3 & \text{} & 2 & \text{} & \text{} & \text{} & \text{} & \text{} & 1 \end{array} \right)$

Row products of the matrix above are the natural numbers.