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A106614
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a(n) = numerator of n/(n+13).
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20
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 3, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 4, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 5, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75
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OFFSET
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0,3
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COMMENTS
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In general, the numerators of n/(n+p) for prime p and n >= 0, form a sequence with the g.f.: x/(1-x)^2 - (p-1)*x^p/(1-x^p)^2. - Paul D. Hanna, Jul 27 2005
a(n) <> n iff n = 13 * k, in this case, a(n) = k. - Bernard Schott, Feb 19 2019
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,-1).
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FORMULA
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G.f.: x/(1-x)^2 - 12*x^13/(1-x^13)^2. - Paul D. Hanna, Jul 27 2005
Dirichlet g.f.: zeta(s-1)*(1-12/13^s). - R. J. Mathar, Apr 18 2011
Multiplicative with a(13^e) = 13^(e-1), and a(p^e) = p^e if p != 13.
Sum_{k=1..n} a(k) ~ (157/338) * n^2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 25*log(2)/13. - Amiram Eldar, Sep 08 2023
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MAPLE
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MATHEMATICA
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PROG
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(Sage) [lcm(n, 13)/13for n in range(0, 100)] # Zerinvary Lajos, Jun 09 2009
(PARI) vector(100, n, n--; numerator(n/(n+13))) \\ G. C. Greubel, Feb 19 2019
(GAP) List([0..80], n->NumeratorRat(n/(n+13))); # Muniru A Asiru, Feb 19 2019
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CROSSREFS
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KEYWORD
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nonn,frac,mult,easy
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AUTHOR
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STATUS
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approved
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