A093880 a(n) = lcm(1, 2, ..., 2n) / lcm(1, 2, ..., n).

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

Offset: 1

Author

Amarnath Murthy, Apr 22 2004

Keywords

• nonn

Comments

Also, lcm(n+1, n+2, ..., 2n-1, 2n) / lcm(1, 2, ..., n-1, n).

Examples

			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.
		

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
• Index entries for sequences related to lcm's

Crossrefs

Cf. A080397.

Programs

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 *)

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).

Extensions

More terms from Emeric Deutsch, Feb 02 2006

Entry revised by N. J. A. Sloane, Jan 24 2007