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A333655
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Highly composite numbers (A002182) that are not superior highly composite numbers (A002201)
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1
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1, 4, 24, 36, 48, 180, 240, 720, 840, 1260, 1680, 7560, 10080, 15120, 20160, 25200, 27720, 45360, 50400, 83160, 110880, 166320, 221760, 277200, 332640, 498960, 554400, 665280, 1081080, 2162160, 2882880, 3603600, 6486480, 7207200, 8648640, 10810800, 14414400
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OFFSET
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1,2
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COMMENTS
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For a number n to be in this sequence, it must have the following conditions be true, where d(n) represents the number of divisors of n (A000005): d(n) > d(k), for all k < n, and there does not exist a number e > 0 such that d(n)/n^e >= d(k)/k^e for k < n and d(n)/n^e > d(k)/k^e for k > n.
This sequence is the same as A189228 until n=12, for which a(12) = 7560 and A189228(12) = 10080.
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LINKS
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Iain Fox, Table of n, a(n) for n = 1..9780 (calculated using b-files of A002182 and A002201)
David Terr, Superior Highly Composite Number.
Eric W. Weisstein, Highly Composite Number.
Wikipedia, Highly composite number.
Wikipedia, Superior highly composite number.
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EXAMPLE
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4 is in the sequence because it has three factors, more than any preceding number, making it highly composite, but it is not a superior highly composite number.
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PROG
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(PARI) lista(nn)=my(v, w=[1, 2, 4], r=1, p=primes(primepi(2^log(nn)))); v=setminus(Set(vector(nn, i, prod(n=1, primepi(2^log(i)), p[n]^floor(1/(p[n]^(1/log(i))-1))))), [1]); forstep(x=6, v[#v], 6, if(numdiv(x)>r, r=numdiv(x); w=setunion(w, [x]))); setminus(w, v)
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CROSSREFS
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Cf. A000005, A189228.
Highly composite numbers: A002182.
Superior highly composite numbers: A002201.
Sequence in context: A166727 A229295 A007544 * A189228 A338786 A048188
Adjacent sequences: A333652 A333653 A333654 * A333656 A333657 A333658
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KEYWORD
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nonn
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AUTHOR
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Iain Fox, Aug 23 2020
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STATUS
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approved
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