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A025547
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Least common multiple of {1,3,5,...,2n-1}.
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26
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1, 3, 15, 105, 315, 3465, 45045, 45045, 765765, 14549535, 14549535, 334639305, 1673196525, 5019589575, 145568097675, 4512611027925, 4512611027925, 4512611027925, 166966608033225, 166966608033225, 6845630929362225
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OFFSET
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1,2
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COMMENTS
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This sequence coincides with the sequence f(n) = denominator of 1+1/3+1/5+1/7+...+1/(2n-1) iff n <= 38. But a(39) = 6414924694381721303722858446525, f(39) = 583174972216520118520259858775. - T. D. Noe, Aug 04 2004
Coincides for n=1..42 with the denominators of a series for Pi*sqrt(2)/4 and then starts to differ. See A127676.
a(floor((n+1)/2)) = GCD(a(n), A051426(n)). [Reinhard Zumkeller, Apr 25 2011]
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..200
Index entries for sequences related to lcm's
Eric Weisstein's World of Mathematics, Jeep Problem, Pi, Pi Continued Fraction, Least Common Multiple
Wikipedia, Least common multiple
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MAPLE
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A025547:=proc(n) local i, t1; t1:=1; for i from 1 to n do t1:=lcm(t1, 2*i-1); od: t1; end;
f := n->denom(add(1/(2*k-1), k=0..n)); # a different sequence!
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MATHEMATICA
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a = 1; Join[{1}, Table[a = LCM[a, n], {n, 3, 125, 2}]] (* From Zak Seidov, Jan 18 2011 *)
nn=30; With[{c=Range[1, 2*nn, 2]}, Table[LCM@@Take[c, n], {n, nn}]] (* Harvey P. Dale, Jan 27 2013 *)
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PROG
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(Haskell)
a025547 n = foldl lcm 1 [1, 3..2*n-1] -- Reinhard Zumkeller, Apr 25 2011
(PARI) a(n)=lcm(vector(n, k, 2*k-1)) \\ Charles R Greathouse IV, Nov 20 2012
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CROSSREFS
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Cf. A007509, A025550, A075135. The numerators are in A074599.
Cf. A003418 (LCM of {1..n}).
Sequence in context: A136092 A181131 A145624 * A220747 A088989 A001801
Adjacent sequences: A025544 A025545 A025546 * A025548 A025549 A025550
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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