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Search: id:A051696
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| A051696 |
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Greatest common divisor of n! and n^n. |
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+0
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; listen)
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OFFSET
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1,2
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COMMENT
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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
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T. D. Noe, Table of n, a(n) for n=1..500
Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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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
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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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CROSSREFS
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Sequence in context: A112283 A136182 A067911 this_sequence A066570 A073656 A047930
Adjacent sequences: A051693 A051694 A051695 this_sequence A051697 A051698 A051699
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Leroy Quet
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 08 1999
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