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.

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