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A025550
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a(n) = ( 1/1 + 1/3 + 1/5 + ... + 1/(2*n-1) )*LCM(1, 3, 5, ..., 2*n-1).
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9
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1, 4, 23, 176, 563, 6508, 88069, 91072, 1593269, 31037876, 31730711, 744355888, 3788707301, 11552032628, 340028535787, 10686452707072, 10823198495797, 10952130239452, 409741429887649, 414022624965424, 17141894231615609
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OFFSET
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1,2
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COMMENTS
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Or, numerator of 1/1 + 1/3 + ... + 1/(2n-1) up to a(38).
Following similar remark by T. D. Noe in A025547, this coincides with f(n) = numerator of 1+1/3+1/5+1/7+...+1/(2n-1) iff n <= 38. But a(39) = 18048708369314455836683437302413, f(39)=1640791669937677803334857936583. Note that f(n)=numerator(digamma(n+1/2)/2+log(2)+euler_gamma/2). - Paul Barry, Aug 19 2005
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LINKS
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Jean-François Alcover, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Jeep Problem
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MAPLE
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a:= n-> (f-> add(1/p, p=f)*ilcm(f[]))([2*i-1$i=1..n]):
seq(a(n), n=1..40); # Alois P. Heinz, Apr 16 2015
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MATHEMATICA
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With[{odds=Range[1, 71, 2]}, Table[Total[1/Take[odds, n]]LCM@@Take[odds, n], {n, 30}]] (* Harvey P. Dale, Aug 21 2011 *)
(* Only up to a(38) *) Numerator[Accumulate[1/Range[1, 2*38-1, 2]]] (* Harvey P. Dale, Mar 30 2015, updated by Jean-François Alcover, Apr 16 2015 *)
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PROG
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(Haskell)
a025550 n = numerator $ sum $ map (1 %) $ take n [1, 3 ..]
-- Reinhard Zumkeller, Jan 22 2012
(PARI) a(n)=my(v=vector(n, i, 2*i-1)); sum(i=1, #v, 1/v[i])*lcm(v) \\ Charles R Greathouse IV, Feb 28 2013
(MAGMA) [&+[1/d: d in i]*Lcm(i) where i is [1..2*n-1 by 2]: n in [1..21]]; // Bruno Berselli, Apr 16 2015
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CROSSREFS
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Cf. A025547, A075135, A002428.
Sequence in context: A127131 A083355 A141763 * A067545 A004041 A220353
Adjacent sequences: A025547 A025548 A025549 * A025551 A025552 A025553
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KEYWORD
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nonn,easy,nice,frac
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AUTHOR
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Clark Kimberling
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EXTENSIONS
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Value of a(39) corrected by Jean-François Alcover, Apr 16 2015
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STATUS
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approved
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