%I #47 Nov 25 2022 13:17:16

%S 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,

%T 29,5,31,16,11,17,35,2,37,19,13,20,41,7,43,22,5,23,47,8,49,25,17,26,

%U 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

%N a(n) = numerator of n/(n+18).

%C 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

%H G. C. Greubel, <a href="/A106619/b106619.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, 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).

%F a(n) = 2*a(n-18) - a(n-36). - _Paul Curtz_, Feb 27 2011

%F Nonasection: a(9*n) = A026741(n). - _Paul Curtz_, Mar 21 2011

%F 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

%F a(n) = n/gcd(n,18), n >= 0. See the harmonic mean comment above, and the _Zerinvary Lajos_ program below. - _Wolfdieter Lang_, Jul 04 2013

%F a(n+3) = A227042(n+3,3), n >= 0. - _Wolfdieter Lang_, Jul 04 2013

%F From _Amiram Eldar_, Nov 25 2022: (Start)

%F 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.

%F Sum_{k=1..n} a(k) ~ (61/216) * n^2. (End)

%p seq(numer(n/(n+18)),n=0..80); # _Muniru A Asiru_, Feb 19 2019

%t f[n_]:=Numerator[n/(n+18)];Array[f,100,0] (* _Vladimir Joseph Stephan Orlovsky_, Feb 17 2011 *)

%o (Sage) [lcm(n,18)/18 for n in range(0, 100)] # _Zerinvary Lajos_, Jun 12 2009

%o (Magma) [Numerator(n/(n+18)): n in [0..100]]; // _Vincenzo Librandi_, Apr 18 2011

%o (PARI) vector(100, n, n--; numerator(n/(n+18))) \\ _G. C. Greubel_, Feb 19 2019

%o (GAP) List([0..80],n->NumeratorRat(n/(n+18))); # _Muniru A Asiru_, Feb 19 2019

%Y Cf. Sequences given by the formula numerator(n/(n + k)): A026741 (k = 2), A051176 (k = 3), A060819 (k = 4), A060791 (k = 5), A060789 (k = 6), A106608 thru A106612 (k = 7 thru 11), A051724 (k = 12), A106614 thru A106621 (k = 13 thru 20).

%Y Cf. A227042.

%K nonn,easy,frac,mult

%O 0,5

%A _N. J. A. Sloane_, May 15 2005