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Search: id:A093880
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| A093880 |
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LCM(1, 2, ..., 2n)/LCM(1, 2, ..., n). |
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+0
3
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also, LCM(n+1,n+2,...,2n-1,2n)/LCM(1,2,...,n-1,n).
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REFERENCES
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J. Sondow, Criteria for irrationality of Euler's constant, Proc. Amer. Math. Soc. 131 (2003) 3335-3344.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..500
J. Sondow, Criteria for irrationality of Euler's constant
Eric Weisstein's World of Mathematics, Least Common Multiple
Index entries for sequences related to lcm's
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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, ln(a(n))/n -> 1 as n -> infinity. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 17 2005
a(n) = A003418(2n)/A003418(n) = A099996(n)/A003418(n).
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EXAMPLE
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LCM of {1,2,3,4,5,6} is 60 and 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); (Deutsch)
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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}] (from Robert G. Wilson v Jan 22 2005)
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CROSSREFS
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Cf. A080397.
Sequence in context: A095107 A115113 A163788 this_sequence A080397 A048782 A083458
Adjacent sequences: A093877 A093878 A093879 this_sequence A093881 A093882 A093883
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 22 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 02 2006
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Jan 24 2007
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