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A051696
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Greatest common divisor of n! and n^n.
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5
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1, 2, 3, 8, 5, 144, 7, 128, 81, 6400, 11, 248832, 13, 100352, 91125, 32768, 17, 429981696, 19, 163840000, 6751269, 63438848, 23, 247669456896, 15625, 1417674752, 1594323, 80564191232, 29, 25076532510720000000, 31, 2147483648
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) also equals the smallest positive integer such that LCM(a(1),a(2),a(3),...a(n)) = n!, for every positive integer n. - Leroy Quet Apr 28 2007
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..500
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FORMULA
| a(n) = product{p|n} p^(sum{k>=1} floor(n/p^k)), where the product is over the distinct primes p that divide n. - Leroy Quet Apr 28 2007
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EXAMPLE
| a[4]=8 since 4!=24 and 4^4=256 and GCD(24,256)=8
LCM(a(1),a(2),a(3),a(4),a(5),a(6)) = LCM(1,2,3,8,5,144) = 6! = 720. (See comment.)
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MATHEMATICA
| Table[GCD[n!, n^n], {n, 40}] (* From Harvey P. Dale, Oct 20 2011 *)
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CROSSREFS
| Sequence in context: A136182 A170911 A067911 * A066570 A073656 A047930
Adjacent sequences: A051693 A051694 A051695 * A051697 A051698 A051699
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Leroy Quet
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 08 1999
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