Vipul at 23:13, 23 July 2022

2022-07-23T23:13:12Z

← Older revision		Revision as of 23:13, 23 July 2022
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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"/>

Vipul: Created page with '{{natural number property}} ==Definition== A natural number $n$ is termed a '''highly composite number''' if it is a [[defining ingredient::strict maximum-so-far...'

2009-04-29T02:48:36Z

Created page with '{{natural number property}} ==Definition== A natural number <math>n</math> is termed a '''highly composite number''' if it is a [[defining ingredient::strict maximum-so-far...'

New page

{{natural number property}}

==Definition==

A [[natural number]] <math>n</math> is termed a '''highly composite number''' if it is a [[defining ingredient::strict maximum-so-far]] for the [[defining ingredient::divisor count function]]. In other words, if <math>\tau(n)</math> denotes the number of divisors of <math>n</math>, then <math>n</math> is highly composite if <math>\tau(n) > \tau(k)</math> for every natural number <math>k < n</math>.

==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.

Highly composite number - Revision history

Vipul at 23:13, 23 July 2022

Vipul: Created page with '{{natural number property}} ==Definition== A natural number n is termed a '''highly composite number''' if it is a [[defining ingredient::strict maximum-so-far...'

Vipul: Created page with '{{natural number property}} ==Definition== A natural number $n$ is termed a '''highly composite number''' if it is a [[defining ingredient::strict maximum-so-far...'