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A061055 Factorial splitting: write n! = x*y with x<y and x maximal; sequence gives value of x. 9
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; text; internal format)
OFFSET

2,2

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. - Zak Seidov, Jul 07 2009

LINKS

Table of n, a(n) for n=2..27.

EXAMPLE

6! = 24*30, with difference of 6.

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

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} ]

CROSSREFS

Cf. A061056-A061060, A061030-A061033, A200743.

Sequence in context: A148089 A200743 A060776 * A148090 A148091 A123420

Adjacent sequences:  A061052 A061053 A061054 * A061056 A061057 A061058

KEYWORD

nonn

AUTHOR

Ed Pegg Jr, May 28 2001

EXTENSIONS

More terms from Dean Hickerson, Jun 13, 2001

More terms from Zak Seidov, Jul 07 2009

a(2)=1 added by Nathaniel Johnston, Jun 25 2011

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)