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 A106611 #33 Nov 25 2022 13:17:48
%S A106611 0,1,1,3,2,1,3,7,4,9,1,11,6,13,7,3,8,17,9,19,2,21,11,23,12,5,13,27,14,
%T A106611 29,3,31,16,33,17,7,18,37,19,39,4,41,21,43,22,9,23,47,24,49,5,51,26,
%U A106611 53,27,11,28,57,29,59,6,61,31,63,32,13,33,67,34,69,7,71,36,73,37,15,38,77,39
%N A106611 a(n) = numerator of n/(n+10).
%C A106611 A strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for n,m >= 1. It follows that a(n) is a divisibility sequence: if n divides m then a(n) divides a(m). - _Peter Bala_, Feb 17 2019
%H A106611 Muniru A Asiru, <a href="/A106611/b106611.txt">Table of n, a(n) for n = 0..5000</a>
%H A106611 Wikipedia, <a href="https://en.wikipedia.org/wiki/Quasi-polynomial">Quasi-polynomial</a>.
%H A106611 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,-1).
%F A106611 From _R. J. Mathar_, Apr 18 2011: (Start)
%F A106611 a(n) = A109051(n)/10.
%F A106611 Dirichlet g.f.: zeta(s-1)*(1 - 4/5^s - 1/2^s + 4/10^s).
%F A106611 Multiplicative with a(2^e) = 2^max(0,e-1), a(5^e) = 5^max(0,e-1), a(p^e) = p^e if p = 3 or p >= 7. (End)
%F A106611 From _Peter Bala_, Feb 17 2019: (Start)
%F A106611 a(n) = numerator(n/((n + 2)*(n + 5))).
%F A106611 a(n) = n/b(n), where b(n) = [1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, ...] is a purely periodic sequence of period 10. Thus a(n) is a quasi-polynomial in n.
%F A106611 If gcd(n,m) = 1 then a( a(n)*a(m) ) = a(a(n)) * a(a(m)), a( a(a(n))*a(a(m)) ) = a(a(a(n))) * a(a(a(m))) and so on.
%F A106611 O.g.f.: Sum_{d divides 10} A023900(d)*x^d/(1 - x^d)^2 = x/(1 - x)^2 - x^2/(1 - x^2)^2 - 4*x^5/(1 - x^5)^2 + 4*x^10/(1 - x^10)^2.
%F A106611 (End)
%F A106611 Sum_{k=1..n} a(k) ~ (63/200) * n^2. - _Amiram Eldar_, Nov 25 2022
%t A106611 f[n_]:=Numerator[n/(n+10)];Array[f,100,0] (* _Vladimir Joseph Stephan Orlovsky_, Feb 17 2011 *)
%o A106611 (Sage) [lcm(n,10)/10 for n in range(0, 79)] # _Zerinvary Lajos_, Jun 07 2009
%o A106611 (Magma) [Numerator(n/(n+10)): n in [0..100]]; // _Vincenzo Librandi_, Apr 18 2011
%o A106611 (GAP) List([0..80],n->NumeratorRat(n/(n+10))); # _Muniru A Asiru_, Feb 18 2019
%Y A106611 Cf. A023900, A109051, A303367.
%Y A106611 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 A106611 nonn,easy,frac,mult
%O A106611 0,4
%A A106611 _N. J. A. Sloane_, May 15 2005