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A106609
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Numerator of n/(n+8).
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3
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0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 2, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 4, 33, 17, 35, 9, 37, 19, 39, 5, 41, 21, 43, 11, 45, 23, 47, 6, 49, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 15, 61, 31, 63, 8, 65, 33, 67, 17, 69, 35, 71, 9, 73, 37, 75, 19, 77, 39, 79
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The graph of this sequence is made up of four linear functions: a(n_odd)=n, a(n=2+4i)=n/2, a(4+8i)=n/4, a(8i)=n/8. Zak Seidov (zakseidov!ahoo.com), Oct 30, 2006. In general, f(n) = numerator of n/(n+m) consists of linear functions n/d_i, where d_i are divisors of m (including 1 and m).
Multiplicative with a(2^e) = 2^max(0,e-3). a(p^e) = p^e if p>2. - R. J. Mathar, Apr 18 2011
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 0..10000
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FORMULA
| a(n)= +2*a(n-8) -a(n-16).
G.f.: x* (x^2-x+1) * (x^12 +2*x^11 +4*x^10 +3*x^9 +4*x^8 +4*x^7 +7*x^6 +4*x^5 +4*x^4 +3*x^3 +4*x^2 +2*x +1) / ( (x-1)^2 *(1+x)^2 *(x^2+1)^2 *(x^4+1)^2 ). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 02 2010
a(n) = A109049(n)/8. Dirichlet g.f. zeta(s-1)*(1-1/2^s-1/2^(2s)-1/2^(3s)). - R. J. Mathar, Apr 18 2011
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MAPLE
| with(finance):seq(numer(cashflows( [1, 1, n], 1 )), n=-6..73); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2008
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MATHEMATICA
| f[n_]:=Numerator[n/(n+8)]; Array[f, 100, 0] (*From Vladimir Joseph Stephan Orlovsky, Feb 16 2011*)
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PROG
| (Other) sage: [lcm(n, 8)/8for n in xrange(0, 80)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 09 2009]
(MAGMA) [Numerator(n/(n+8)): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011
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CROSSREFS
| Cf. A109049.
Sequence in context: A000265 A106617 A040026 * A171968 A093474 A030101
Adjacent sequences: A106606 A106607 A106608 * A106610 A106611 A106612
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KEYWORD
| nonn,frac,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 15 2005
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