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A056038 Largest factorial k! such that (k!)^2 divides n!. 4
1, 1, 1, 2, 2, 6, 6, 24, 24, 720, 720, 720, 720, 5040, 5040, 40320, 40320, 362880, 362880, 3628800, 3628800, 39916800, 39916800, 479001600, 479001600, 6227020800, 6227020800, 1307674368000, 1307674368000, 1307674368000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This is neither floor(n/2)! nor ceiling(n/2), but often coincidence with one of them.

a(n)=x!, where x = floor(n/2) + d(n) and d=0,1,2,... Below 1000, d=1 arises 93 times, d=2 4 times.

A105350(n) = a(n)^2.

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

For n=10 or n=11, floor(n/2)! = 5! = 120; 5!^2 = 14400 divides 10! = 14400*252 or 11! = 14400*2772. However, 10!/6!^2 = 7 and 11!/6!^2 = 77, i.e., (d + floor(n/2))^2 may divide n!. Here d=1, but d > 1 also occurs as follows: for n=416 or n=417, floor(n/2)=208, and 208!^2 divides 416! and 417!, but 209!^2 and 210!^2 also divide these factorials.

CROSSREFS

Cf. A000142, A001057, A001405, A055772, A056039.

Sequence in context: A132369 A282169 A081123 * A076929 A265642 A186944

Adjacent sequences:  A056035 A056036 A056037 * A056039 A056040 A056041

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 25 2000

STATUS

approved

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Last modified September 20 11:26 EDT 2020. Contains 337264 sequences. (Running on oeis4.)