Highly composite number: Difference between revisions
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* [[Superabundant number]] is a closely related notion -- it is a [[strict maximum-so-far]] for the ratio of the [[divisor sum function]] to the number itself. | * [[Superabundant number]] is a closely related notion -- it is a [[strict maximum-so-far]] for the ratio of the [[divisor sum function]] to the number itself. | ||
==Occurrence== | |||
===Initial values=== | |||
<section begin="list"/>[[1]], [[2]], [[4]], [[6]], [[12]], [[24]], [[36]], [[48]], [[60]], [[120]], [[180]], [[240]], [[360]], [[720]], <toggledisplay>840, 1260, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160</toggledisplay>[[Oeis:A002182|View list on OEIS]]<section end="list"/> | |||
Latest revision as of 23:13, 23 July 2022
This article defines a property that can be evaluated for a natural number, i.e., every natural number either satisfies the property or does not satisfy the property.
View a complete list of properties of natural numbers
Definition
A natural number is termed a highly composite number if it is a strict maximum-so-far for the divisor count function. In other words, if denotes the number of divisors of , then is highly composite if for every natural number .
Relation with other properties
- Superabundant number is a closely related notion -- it is a strict maximum-so-far for the ratio of the divisor sum function to the number itself.
Occurrence
Initial values
1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, [SHOW MORE]