Prime and composite numbers Education is the most important
A superior highly composite number is a positive integer n n for which there is an ϵ > 0 ϵ > 0 such that d(n) nϵ ≥ d(k) kϵ d ( n) n ϵ ≥ d ( k) k ϵ for all k > 1 k > 1, where the function d(n) d ( n) counts the divisors of n n.
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1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 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 ( list ; graph ; refs ; listen ; history ; text ; internal format )
Highly composite numbers
For s=1, these numbers have been called superabundant by L. Alaoglu and P. Erdős , , and the generalized superior highly composite numbers have been called colossally abundant. The real solution of 2 s +4 s +8 s =3 s +9 s is approximately 1.6741. 10.60. For s=1, the results of this and the following section are in and . 10.62.
Math Calculating Highly Composite Numbers (AntiPrimes) YouTube
The first several superior highly composite numbers are 2, 6, 12, 60, 120, 360. The sequence is http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=002201A002201 in Sloane's encyclopedia. References 1L. Alaoglu and P. Erdös, On highly composite and similar numbers. Trans. Amer. Math. Soc. 56(1944), 448-469.
Superior highly composite number Detailed Pedia
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[Solved] Are all highly composite numbers even? 9to5Science
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised to some positive power.
Highly composite numbers
There are an infinite number of highly composite numbers, and the first few are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040,. (OEIS A002182 ). The corresponding numbers of divisors are 1, 2, 3, 4, 6, 8, 9, 10, 12, 16, 18, 20, 24, 30, 32,. (OEIS A002183 ).
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A superior highly composite number is a natural number which has more divisors than any other
Superior highly composite numbers: positive integers n for which there is an e > 0 such that d (n)/n^e >= d (k)/k^e for all k > 1, where the function d (n) counts the divisors of n ( A000005 ). (Formerly M1591 N0620) 43
Highly Composite Numbers
A superior highly composite number is a positive integer n for which there is an e>0 such that (d (n))/ (n^e)>= (d (k))/ (k^e) for all k>1, where the function d (n) counts the divisors of n (Ramanujan 1962, pp. 87 and 115).
Composite Numbers
For a superior highly composite number n there exists a positive real number ε such that for all natural numbers k smaller than n we have. and for all natural numbers k larger than n we have. where d(n), the divisor function, denotes the number of divisors of n.The term was coined by Ramanujan (1915).. The first 15 superior highly composite numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440.
MegaFavNumbers superior highly composite numbers and roundness YouTube
In mathematics, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it's defined by a ratio between the number of divisors an integer has and that integer raised to some positive power.
Superior highly composite number Alchetron, the free social encyclopedia
A superior highly composite number is a natural number which has more divisors than any other number scaled relative to the number itself. number-theory elementary-number-theory prime-numbers divisibility divisor-sum Share Cite Follow asked Sep 6, 2014 at 23:22 Omega Force 822 5 14 1
Peter Karpov on Twitter "All possible ways of dividing superior highly composite numbers (60
A number is superior highly composite whenever it has the largest SHCN score for some positive e - when it can be given some disadvantage with the smaller numbers and still have a higher divisor score. The first highly composite number that fails this is 24. It has 8 divisors, and for any e, 8 / 24 e makes this score smaller than for some.
Numbers
When s= 1 these numbers have been called colossally abundant by Erd}os and Alaoglu. It is easily seen that all generalized superior highly composite numbers are generalized highly composite. The prime factorization of a generalized superior highly composite number Ncan be obtained from the value of the parameter ". For r= 1;2;3:::, Ramanujan de.
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A highly composite number is a positive integer with more divisors than any smaller positive integer has. A related concept is that of a largely composite number, a positive integer which has at least as many divisors as any smaller positive integer.
