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A051696
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Greatest common divisor of n! and n^n.
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6
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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
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OFFSET
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1,2
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COMMENTS
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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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FORMULA
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a(n) = Product_{p|n} p^(sum{k >= 1} floor(n/p^k)), where the product runs over the distinct primes p that divide n. - Leroy Quet, Apr 28 2007
a(n) = (numerator of B(n, 1/n))/n^(n - 1), where B(.,.) is the Euler beta function. - Arkadiusz Wesolowski, Nov 22 2017
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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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MAPLE
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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