This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A106620 #37 Sep 08 2023 07:33:30
%S A106620 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,20,21,22,23,24,25,
%T A106620 26,27,28,29,30,31,32,33,34,35,36,37,2,39,40,41,42,43,44,45,46,47,48,
%U A106620 49,50,51,52,53,54,55,56,3,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74
%N A106620 a(n) = numerator of n/(n+19).
%C A106620 a(n) <> n iff n = 19 * k, in this case, a(n) = k. - _Bernard Schott_, Feb 19 2019
%H A106620 G. C. Greubel, <a href="/A106620/b106620.txt">Table of n, a(n) for n = 0..10000</a>
%H A106620 <a href="/index/Rec#order_38">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).
%F A106620 Dirichlet g.f.: zeta(s-1)*(1 - 18/19^s). - _R. J. Mathar_, Apr 18 2011
%F A106620 a(n) = 2*a(n-19) - a(n-38). - _G. C. Greubel_, Feb 19 2019
%F A106620 From _Amiram Eldar_, Nov 25 2022: (Start)
%F A106620 Multiplicative with a(19^e) = 19^(e-1), and a(p^e) = p^e if p != 19.
%F A106620 Sum_{k=1..n} a(k) ~ (343/722) * n^2. (End)
%F A106620 Sum_{n>=1} (-1)^(n+1)/a(n) = 37*log(2)/19. - _Amiram Eldar_, Sep 08 2023
%p A106620 seq(numer(n/(n+19)),n=0..80); # _Muniru A Asiru_, Feb 19 2019
%t A106620 f[n_]:=Numerator[n/(n+19)];Array[f,100,0] (* _Vladimir Joseph Stephan Orlovsky_, Feb 17 2011 *)
%o A106620 (Sage) [lcm(n,19)/19 for n in range(0, 100)] # _Zerinvary Lajos_, Jun 12 2009
%o A106620 (Magma) [Numerator(n/(n+19)): n in [0..100]]; // _Vincenzo Librandi_, Apr 18 2011
%o A106620 (PARI) vector(100, n, n--; numerator(n/(n+19))) \\ _G. C. Greubel_, Feb 19 2019
%o A106620 (GAP) List([0..80],n->NumeratorRat(n/(n+19))); # _Muniru A Asiru_, Feb 19 2019
%Y A106620 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).
%K A106620 nonn,easy,frac,mult
%O A106620 0,3
%A A106620 _N. J. A. Sloane_, May 15 2005