Highly composite equal division: Difference between revisions

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{{EDOs|180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560}}, <br>

10080, 15120, 20160, 25200, [[27720edo|27720]], 45360, 50400, 55440, 83160, 110880, <br>

166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160.

166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, [[Tel:1081080|1081080]], [[Tel:1441440|1441440]], 2162160.

Superabundant edos that are also highly composite, excluding the first 19: 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 665280, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 8648640, 10810800, 21621600, 36756720, 61261200, 73513440, 122522400, 147026880, 183783600, 367567200, 698377680, 735134400. The sequence is finite and has 430 terms starting with 10080.

Superabundant edos that are also highly composite, excluding the first 19: 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 665280, 720720, [[Tel:1441440|1441440]], 2162160, 3603600, 4324320, 7207200, 8648640, 10810800, 21621600, 36756720, 61261200, 73513440, 122522400, 147026880, 183783600, 367567200, 698377680, 735134400. The sequence is finite and has 430 terms starting with 10080.

== Highly composite EDF ==

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Prominence (term proposed by Eliora) is the product of the number's count of divisors (highly composite) or its abundance index (superabundant) with its amount of distinct prime factors. Prominence serves as a good measure of different varieties of subsets that an equal division can provide, since a more prominent number is capable of approximating more distinct temperaments efficiently for its size.

Example: [[1848edo]] is more prominent than [[3456edo]] despite both having 32 divisors, due to 1848 having 2, 3~~, 5~~, 7, and 11 as prime factors, while 3456 having only 2 and 3.

Example: [[1848edo]] is more prominent than [[3456edo]] despite both having 32 divisors, due to 1848 having 2, 3, 7, and 11 as prime factors, while 3456 having only 2 and 3.

Just as there are generalized N-highly composite numbers, one can generalize N,M-highly prominent numbers, since this time there is another dimension.

@@ Line 23: / Line 23: @@
 {{EDOs|180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560}}, <br>
 , 15120, 20160, 25200, [[27720edo|27720]], 45360, 50400, 55440, 83160, 110880, <br>
-, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160.
+, 221760, 277200, 332640, 498960, 554400, 665280, 720720, [[Tel:1081080|1081080]], [[Tel:1441440|1441440]], 2162160.
-Superabundant edos that are also highly composite, excluding the first 19: 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 665280, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 8648640, 10810800,  21621600, 36756720, 61261200, 73513440, 122522400, 147026880, 183783600, 367567200, 698377680, 735134400. The sequence is finite and has 430 terms starting with 10080.
+Superabundant edos that are also highly composite, excluding the first 19: 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 665280, 720720, [[Tel:1441440|1441440]], 2162160, 3603600, 4324320, 7207200, 8648640, 10810800,  21621600, 36756720, 61261200, 73513440, 122522400, 147026880, 183783600, 367567200, 698377680, 735134400. The sequence is finite and has 430 terms starting with 10080.
 == Highly composite EDF ==
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 Prominence (term proposed by Eliora) is the product of the number's count of divisors (highly composite) or its abundance index (superabundant) with its amount of distinct prime factors. Prominence serves as a good measure of different varieties of subsets that an equal division can provide, since a more prominent number is capable of approximating more distinct temperaments efficiently for its size.
-Example: [[1848edo]] is more prominent than [[3456edo]] despite both having 32 divisors, due to 1848 having 2, 3, 5, 7, and 11 as prime factors, while 3456 having only 2 and 3.
+Example: [[1848edo]] is more prominent than [[3456edo]] despite both having 32 divisors, due to 1848 having 2, 3, 7, and 11 as prime factors, while 3456 having only 2 and 3.
 Just as there are generalized N-highly composite numbers, one can generalize N,M-highly prominent numbers, since this time there is another dimension.