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A056038
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Largest factorial k! such that (k!)^2 divides n!.
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4
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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; internal format)
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OFFSET
| 1,4
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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.
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EXAMPLE
| 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 occur as follows: n=416 or n=417, Floor[n/2]=208, 208!^2 divides 416! or 417!, but 209!^2 and 210!^2 also divide these factorials.
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CROSSREFS
| Cf. A000142, A001057, A001405, A055772, A056039.
Sequence in context: A129881 A132369 A081123 * A076929 A174789 A062073
Adjacent sequences: A056035 A056036 A056037 * A056039 A056040 A056041
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 25 2000
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