This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060777 #30 Dec 10 2024 18:00:13
%S A060777 1,2,3,6,12,30,72,210,630,1920,6336,22176,78975,295680,1144000,
%T A060777 4576000,18869760,80061696,348986880,1560176640,7148445696,
%U A060777 33530112000,160813154304,787718131200,3938590656000,20083261440000,104351051284480,552173794099200,2973519499493376,16286922357866496,90680032493568000,512971179263262720
%N A060777 Larger central (or median) divisor of n!.
%C A060777 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 A060777 The integer part of square root of n! (A055226(n)) is situated between x and y.
%H A060777 Max Alekseyev, <a href="/A060777/b060777.txt">Table of n, a(n) for n = 1..140</a>
%H A060777 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 A060777 a(n) = A033677(A000142(n)). - _Pontus von Brömssen_, Jul 15 2023
%F A060777 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 A060777 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 A060777 Table[ Part[ Divisors[ w! ], 1+Floor[ DivisorSigma[ 0, n! ]/2 ] ], {w, a, b} ]
%Y A060777 Cf. A027423, A055226, A000196, A000142, A000005, A060776, A061057, A033677.
%K A060777 nonn
%O A060777 1,2
%A A060777 _Labos Elemer_, Apr 26 2001
%E A060777 More terms from _Don Reble_, Dec 13 2001