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
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
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