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 A093880 a(n) = lcm(1, 2, ..., 2n) / lcm(1, 2, ..., n). 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also, lcm(n+1, n+2, ..., 2n-1, 2n) / lcm(1, 2, ..., n-1, n). LINKS T. D. Noe, Table of n, a(n) for n = 1..500 J. Sondow, Criteria for irrationality of Euler's constant, Criteria for irrationality of Euler's constant, Proc. Amer. Math. Soc. 131 (2003) 3335-3344. Eric Weisstein's World of Mathematics, Least Common Multiple FORMULA 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 a(n) = A003418(2n)/A003418(n) = A099996(n)/A003418(n). EXAMPLE 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. MAPLE 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 MATHEMATICA f[n_] := LCM @@ Table[i, {i, 2n}]/LCM @@ Table[i, {i, n}]; Table[ f[n], {n, 27}] (* Robert G. Wilson v, Jan 22 2005 *) CROSSREFS Cf. A080397. Sequence in context: A115113 A163788 A324547 * A080397 A322756 A048782 Adjacent sequences:  A093877 A093878 A093879 * A093881 A093882 A093883 KEYWORD nonn AUTHOR Amarnath Murthy, Apr 22 2004 EXTENSIONS More terms from Emeric Deutsch, Feb 02 2006 Entry revised by N. J. A. Sloane, Jan 24 2007 STATUS approved

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Last modified July 3 06:54 EDT 2022. Contains 355031 sequences. (Running on oeis4.)