Highly composite equal division: Difference between revisions

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== Generalization ==

=== Superabundant equal division ===

[[Wikipedia:Superabundant number|Superabundant numbers]] are slightly different from highly composite numbers, hence superabundant equal divisions can be considered separately from highly composite numbers whenever the properties of superabundant numbers are more relevant in context.

[[Wikipedia:Superabundant number|Superabundant numbers]] are slightly different from highly composite numbers, hence superabundant equal divisions can be considered separately from highly composite numbers whenever the properties of superabundant numbers are more relevant in context. '''Abundancy index''' is the ratio of the sum of divisors of the number to the number itself, and thus superabundant numbers are numbers where these indices increase to a record, and thus are the highest in proportion to the number itself.

Although neither sequence of these numbers is a subset of the other, the first 19 superabundant and highly composite numbers are the same, and there are more common terms further in the sequences. Therefore, many highly composite equal divisions are also superabundant and vice versa, but some equal divisions are only in one of the two categories (or neither at all).

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 == Generalization ==
 === Superabundant equal division ===
-[[Wikipedia:Superabundant number|Superabundant numbers]] are slightly different from highly composite numbers, hence superabundant equal divisions can be considered separately from highly composite numbers whenever the properties of superabundant numbers are more relevant in context.
+[[Wikipedia:Superabundant number|Superabundant numbers]] are slightly different from highly composite numbers, hence superabundant equal divisions can be considered separately from highly composite numbers whenever the properties of superabundant numbers are more relevant in context. '''Abundancy index''' is the ratio of the sum of divisors of the number to the number itself, and thus superabundant numbers are numbers where these indices increase to a record, and thus are the highest in proportion to the number itself.
 Although neither sequence of these numbers is a subset of the other, the first 19 superabundant and highly composite numbers are the same, and there are more common terms further in the sequences. Therefore, many highly composite equal divisions are also superabundant and vice versa, but some equal divisions are only in one of the two categories (or neither at all).