A060777 - OEIS

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A060777

Larger central (or median) divisor of n!.

1, 2, 3, 6, 12, 30, 72, 210, 630, 1920, 6336, 22176, 78975, 295680, 1144000, 4576000, 18869760, 80061696, 348986880, 1560176640, 7148445696, 33530112000, 160813154304, 787718131200, 3938590656000, 20083261440000, 104351051284480, 552173794099200, 2973519499493376, 16286922357866496, 90680032493568000, 512971179263262720

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OFFSET

1,2

COMMENTS

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.

The integer part of square root of n! (A055226(n)) is situated between x and y.

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..140

FORMULA

a(n) = A033677(A000142(n)). - Pontus von Brömssen, Jul 15 2023

EXAMPLE

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.

MATHEMATICA

Table[ Part[ Divisors[ w! ], 1+Floor[ DivisorSigma[ 0, n! ]/2 ] ], {w, a, b} ]

CROSSREFS

Cf. A027423, A055226, A000196, A000142, A000005, A060776, A061057, A033677.

Sequence in context: A261230 A014278 A061056 * A200744 A089430 A337638