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A060776
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Smaller central (median) divisor of n!.
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18
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1, 1, 2, 4, 10, 24, 70, 192, 576, 1890, 6300, 21600, 78848, 294840, 1143072, 4572288, 18849600, 79968000, 348566400, 1559376000, 7147140000, 33522128640, 160758097500, 787652812800, 3938264064000, 20080974513600, 104348440350000, 552160113120000
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OFFSET
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1,3
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COMMENTS
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Factorial splitting: write n! = x*y with x <= y and x maximal; sequence gives value of x. Inequality "x < y" gives the same sequence, except that a(1) is not defined.
Between this d and its complementary divisor, the integer part of square root of n! is situated; for n=6: {24,26,30}. - Nathaniel Johnston, Jun 25 2011
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LINKS
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FORMULA
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EXAMPLE
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Divisors of 6!=720 are {1,2,3,4,5,6,...,24,30,...,360,720}. a(6)=24, the 15th divisor from 30 divisors of 720.
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MATHEMATICA
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Table[ Part[ Divisors[ w! ], Floor[ DivisorSigma[ 0, n! ]/2 ] ], {w, a, b} ]
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PROG
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(PARI) a(n) = if (n==1, 1, my(d=divisors(n!)); d[#d\2]); \\ Michel Marcus, Sep 16 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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