cp's OEIS Frontend

A060776 Smaller central (median) divisor of n!.

%I A060776 #45 Dec 10 2024 17:56:40
%S A060776 1,1,2,4,10,24,70,192,576,1890,6300,21600,78848,294840,1143072,
%T A060776 4572288,18849600,79968000,348566400,1559376000,7147140000,
%U A060776 33522128640,160758097500,787652812800,3938264064000,20080974513600,104348440350000,552160113120000
%N A060776 Smaller central (median) divisor of n!.
%C A060776 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 A060776 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 A060776 Max Alekseyev, <a href="/A060776/b060776.txt">Table of n, a(n) for n = 1..140</a> (first 59 terms from Oleg Terentyev)
%H A060776 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 A060776 a(n) = n!/A060777(n). - _David Wasserman_, Jun 15 2002
%F A060776 a(n) = A033676(A000142(n)). - _Pontus von Brömssen_, Jul 15 2023
%F A060776 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 A060776 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 A060776 Table[ Part[ Divisors[ w! ], Floor[ DivisorSigma[ 0, n! ]/2 ] ], {w, a, b} ]
%o A060776 (PARI) a(n) = if (n==1, 1, my(d=divisors(n!)); d[#d\2]); \\ _Michel Marcus_, Sep 16 2018
%Y A060776 Cf. A027423, A055226, A000196, A000142, A000005, A060777, A033676.
%K A060776 nonn
%O A060776 1,3
%A A060776 _Labos Elemer_, Apr 26 2001
%E A060776 More terms from _David Wasserman_, Jun 15 2002
%E A060776 a(27)-a(32) from _M. F. Hasler_, Sep 20 2011