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A106619
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a(n) = numerator of n/(n+18).
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10
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0, 1, 1, 1, 2, 5, 1, 7, 4, 1, 5, 11, 2, 13, 7, 5, 8, 17, 1, 19, 10, 7, 11, 23, 4, 25, 13, 3, 14, 29, 5, 31, 16, 11, 17, 35, 2, 37, 19, 13, 20, 41, 7, 43, 22, 5, 23, 47, 8, 49, 25, 17, 26, 53, 3, 55, 28, 19, 29, 59, 10, 61, 31, 7, 32, 65, 11, 67, 34, 23, 35, 71, 4, 73, 37, 25, 38, 77, 13, 79
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OFFSET
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0,5
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COMMENTS
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a(n+3), n >= 0, is the denominator of the harmonic mean H(n,3) = 6*n/(n+3). a(n+3) = (n+3)/gcd(n+3,18). - Wolfdieter Lang, Jul 04 2013
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).
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FORMULA
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a(n) = 2*a(n-18) - a(n-36). - Paul Curtz, Feb 27 2011
Dirichlet g.f.: zeta(s-1)*(1 - 2/3^s - 2/9^s - 1/2^s + 2/6^s + 2/18^s). - R. J. Mathar, Apr 18 2011
Multiplicative with a(2^e) = 2^max(0, e-1), a(3^e) = 3^max(0,e-2), and a(p^e) = p^e otherwise.
Sum_{k=1..n} a(k) ~ (61/216) * n^2. (End)
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MAPLE
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MATHEMATICA
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PROG
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(Sage) [lcm(n, 18)/18 for n in range(0, 100)] # Zerinvary Lajos, Jun 12 2009
(PARI) vector(100, n, n--; numerator(n/(n+18))) \\ G. C. Greubel, Feb 19 2019
(GAP) List([0..80], n->NumeratorRat(n/(n+18))); # Muniru A Asiru, Feb 19 2019
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CROSSREFS
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KEYWORD
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nonn,easy,frac,mult
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AUTHOR
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STATUS
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approved
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