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Each index <math>i</math> and exponent <math>j</math> appearing in the prime factorization of a positive integer <math>n</math> is itself a positive integer, and thus has a prime factorization of its own.
Each index <math>i</math> and exponent <math>j</math> appearing in the prime factorization of a positive integer <math>n</math> is itself a positive integer, and thus has a prime factorization of its own.
+
+Continuing with the same example, the index <math>32277</math> has the factorization <math>3 \cdot 7 \cdot 29 \cdot 53 = \text{p}_2^1 \text{p}_4^1 \text{p}_{10}^1 \text{p}_{16}^1.</math> Taking this information together with previously known factorizations allows the following replacements to be made:
+
+{| align="center" cellpadding="6" width="90%"
+|
+<math>\begin{array}{rcl}
+2 & \mapsto & \text{p}_1^1
+\\[6pt]
+3 & \mapsto & \text{p}_2^1
+\\[6pt]
+7 & \mapsto & \text{p}_4^1
+\\[6pt]
+32277 & \mapsto & \text{p}_2^1 \text{p}_4^1 \text{p}_{10}^1 \text{p}_{16}^1
+\end{array}</math>
+|}
==Riffs in Numerical Order==
==Riffs in Numerical Order==
