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%I #27 Jul 15 2023 15:54:29
%S 1,2,3,6,12,30,72,210,630,1920,6336,22176,78975,295680,1144000,
%T 4576000,18869760,80061696,348986880,1560176640,7148445696,
%U 33530112000,160813154304,787718131200,3938590656000,20083261440000,104351051284480,552173794099200,2973519499493376,16286922357866496,90680032493568000,512971179263262720
%N Larger central (or median) divisor of n!.
%C Factorial splitting: write n! = x*y with x <= y and x maximal; sequence gives value of y. Inequality "x < y" gives the same sequence, except that a(1) is not defined.
%C The integer part of square root of n! (A055226(n)) is situated between x and y.
%H Max Alekseyev, <a href="/A060777/b060777.txt">Table of n, a(n) for n = 1..140</a>
%F a(n) = A033677(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)=30, the 16th one from the 30 divisors of 720.
%t Table[ Part[ Divisors[ w! ], 1+Floor[ DivisorSigma[ 0, n! ]/2 ] ], {w, a, b} ]
%Y Cf. A027423, A055226, A000196, A000142, A000005, A060776, A061057, A033677.
%K nonn
%O 1,2
%A _Labos Elemer_, Apr 26 2001
%E More terms from _Don Reble_, Dec 13 2001
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