Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #30 Dec 10 2024 18:00:13
%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>
%H Jean-Marie De Koninck and William Verreault, <a href="https://doi.org/10.2298/PIM2429045D">Arithmetic functions at factorial arguments</a>, Publications de l'Institut Mathematique, Vol. 115, No. 129 (2024), pp. 45-76.
%F a(n) = A033677(A000142(n)). - _Pontus von Brömssen_, Jul 15 2023
%F Sum_{k=1..n} a(k) = sqrt(n!) * (1 + O(1/n^c)), where c < 1 is a positive constant (De Koninck and Verreault, 2024, p. 48, Theorem 2.1). - _Amiram Eldar_, Dec 10 2024
%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