# Difference between revisions of "Highly composite numbers"

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For example, every number above 180 has less factors than has 180, until you get to 240. Then, 240 has an additional two factors over 180. Then, no number above 240 has more factors than 240, until you get to 360, while the quantity of factors of 336 mere ''equals'' that of 240. | For example, every number above 180 has less factors than has 180, until you get to 240. Then, 240 has an additional two factors over 180. Then, no number above 240 has more factors than 240, until you get to 360, while the quantity of factors of 336 mere ''equals'' that of 240. | ||

− | Additionally, the | + | Additionally, the unifying number for all highly composite numbers is 12. This is because of three facts: '''1)''' the ''initiation'' above 6 is always at multiples of twelve but not always at multiples of 6; '''2)''' the initiation span from 12 to 60 is unbroken; and '''3)''' composite equivalence is unbroken from 60 to 120. These three facts together imply a spike graph beginning with 1 and ending with 120, in which there are two sequences of six spikes, in which the ''60 spike'' functions both as the final of the first sequence and as the initial of the second sequence, and the second sequence for which only its first and final numbers are initials. |

## Revision as of 13:23, 6 February 2014

On the opposite extreme from the primes are the highly composite numbers. The primes have the least quantity of factors, namely two. A highly composite number is one which has the greatest quantity of factors compared to any lesser number. In other words, the highly composite numbers each * initiate* an

*increase*in quantity of factors over that of any lesser number.

For example, every number above 180 has less factors than has 180, until you get to 240. Then, 240 has an additional two factors over 180. Then, no number above 240 has more factors than 240, until you get to 360, while the quantity of factors of 336 mere *equals* that of 240.

Additionally, the unifying number for all highly composite numbers is 12. This is because of three facts: **1)** the *initiation* above 6 is always at multiples of twelve but not always at multiples of 6; **2)** the initiation span from 12 to 60 is unbroken; and **3)** composite equivalence is unbroken from 60 to 120. These three facts together imply a spike graph beginning with 1 and ending with 120, in which there are two sequences of six spikes, in which the *60 spike* functions both as the final of the first sequence and as the initial of the second sequence, and the second sequence for which only its first and final numbers are initials.