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A093880
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a(n) = lcm(1, 2, ..., 2n) / lcm(1, 2, ..., n).
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4
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2, 6, 10, 70, 42, 462, 858, 858, 4862, 92378, 8398, 193154, 74290, 222870, 6463230, 200360130, 11785890, 11785890, 22951470, 22951470, 941010270, 40463441610, 1759280070, 82686163290, 115760628606, 115760628606, 2045104438706
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OFFSET
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1,1
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COMMENTS
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Also, lcm(n+1, n+2, ..., 2n-1, 2n) / lcm(1, 2, ..., n-1, n).
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LINKS
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FORMULA
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The prime number theorem implies that a(n) = e^(n(1+o(1))) as n -> infinity. In other words, log(a(n))/n -> 1 as n -> infinity. - Jonathan Sondow, Jan 17 2005
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EXAMPLE
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The LCM of {1,2,3,4,5,6} is 60 and the LCM of {1,2,3} is 6, so a(3) = 60/6 = 10.
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MAPLE
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a:=n->lcm(seq(j, j=n+1..2*n))/lcm(seq(j, j=1..n)): seq(a(n), n=1..32); # Emeric Deutsch, Feb 02 2006
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MATHEMATICA
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f[n_] := LCM @@ Table[i, {i, 2n}]/LCM @@ Table[i, {i, n}]; Table[ f[n], {n, 27}] (* Robert G. Wilson v, Jan 22 2005 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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