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A061055
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Factorial splitting: write n! = x*y with x<y and x maximal; sequence gives value of x.
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10
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| This is essentially the same as A060776; n! is never a perfect square for n>1 so there is always an even number of divisors of n!, so we can list its divisors in increasing order as [d1,d2,...,x,y,...,dk] with x and y the median divisors (A060776 and A060777, respectively). - Nathaniel Johnston, Jun 25 2011
a(27)=104348440350000, a(28)=552160113120000. [From Zak Seidov (zakseidov(AT)yahoo.com), Jul 07 2009]
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EXAMPLE
| 6! = 24*30, with difference of 6.
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MAPLE
| A061055 := proc(n) local d: d:=numtheory[divisors](n!): return d[nops(d)/2]: end: seq(A061055(n), n=2..15); # Nathaniel Johnston, Jun 25 2011
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MATHEMATICA
| Do[ With[ {k = Floor[ Sqrt[ x! ] ] - Do[ If[ Mod[ x!, Floor[ Sqrt[ x! ] ] - n ] == 0, Return[ n ] ], {n, 0, 10000000} ]}, Print[ {x, "! =", k, x!/k, x!/k - k} ] ], {x, 3, 22} ]
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CROSSREFS
| Cf. A061056-A061060, A061030-A061033, A200743.
Sequence in context: A148089 A200743 A060776 * A148090 A148091 A123420
Adjacent sequences: A061052 A061053 A061054 * A061056 A061057 A061058
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KEYWORD
| nonn
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AUTHOR
| Ed Pegg Jr (ed(AT)mathpuzzle.com), May 28 2001
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EXTENSIONS
| More terms from Dean Hickerson (dean.hickerson(AT)yahoo.com), Jun 13, 2001
More terms from Zak Seidov (zakseidov(AT)yahoo.com), Jul 07 2009
a(2)=1 added by Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Jun 25 2011
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