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%I #41 Jul 15 2023 15:54:15
%S 1,1,2,4,10,24,70,192,576,1890,6300,21600,78848,294840,1143072,
%T 4572288,18849600,79968000,348566400,1559376000,7147140000,
%U 33522128640,160758097500,787652812800,3938264064000,20080974513600,104348440350000,552160113120000
%N Smaller central (median) divisor of n!.
%C 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.
%C 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
%H Max Alekseyev, <a href="/A060776/b060776.txt">Table of n, a(n) for n = 1..140</a> (first 59 terms from Oleg Terentyev)
%F a(n) = n!/A060777(n). - _David Wasserman_, Jun 15 2002
%F a(n) = A033676(A000142(n)). - _Pontus von Brömssen_, Jul 15 2023
%e 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.
%t Table[ Part[ Divisors[ w! ], Floor[ DivisorSigma[ 0, n! ]/2 ] ], {w, a, b} ]
%o (PARI) a(n) = if (n==1, 1, my(d=divisors(n!)); d[#d\2]); \\ _Michel Marcus_, Sep 16 2018
%Y Cf. A027423, A055226, A000196, A000142, A000005, A060777, A033676.
%K nonn
%O 1,3
%A _Labos Elemer_, Apr 26 2001
%E More terms from _David Wasserman_, Jun 15 2002
%E a(27)-a(32) from _M. F. Hasler_, Sep 20 2011
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