Superparticular Number
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Superparticular numbers were written about by Nicomachus in his treatise "Introduction to Arithmetic". They are useful in the study of harmony: many musical intervals can be expressed as a superparticular ratio. In this application, Størmer's theorem can be used to list all possible superparticular numbers for a given limit; that is, all ratios of this type in which both the numerator and denominator are smooth numbers.In graph theory, superparticular numbers (or rather, their reciprocals, 1/2, 2/3, 3/4, etc.) arise as the possible values of the upper density of an infinite graph.

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Superparticular numbers were written about by Nicomachus in his treatise "Introduction to Arithmetic". They are useful in the study of harmony: many musical intervals can be expressed as a superparticular ratio. In this application, Størmer's theorem can be used to list all possible superparticular numbers for a given limit; that is, all ratios of this type in which both the numerator and denominator are smooth numbers.In graph theory, superparticular numbers (or rather, their reciprocals, 1/2, 2/3, 3/4, etc.) arise as the possible values of the upper density of an infinite graph.