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 A106616 #38 Nov 25 2022 13:17:35
%S A106616 0,1,2,1,4,1,2,7,8,3,2,11,4,13,14,1,16,17,6,19,4,7,22,23,8,5,26,9,28,
%T A106616 29,2,31,32,11,34,7,12,37,38,13,8,41,14,43,44,3,46,47,16,49,10,17,52,
%U A106616 53,18,11,56,19,58,59,4,61,62,21,64,13,22,67,68,23,14,71,24,73,74,5,76,77,26
%N A106616 Numerator of n/(n+15).
%C A106616 Multiplicative and also a strong divisibility sequence: gcd(a(n),a(m)) = a(gcd(n,m)) for n, m >= 1. - _Peter Bala_, Feb 24 2019
%H A106616 Nathaniel Johnston, <a href="/A106616/b106616.txt">Table of n, a(n) for n = 0..10000</a>
%H A106616 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (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,-1).
%F A106616 Dirichlet g.f.: zeta(s-1)*(1-4/5^s-2/3^s+8/15^s). - _R. J. Mathar_, Apr 18 2011
%F A106616 a(n) = gcd((n-2)*(n-1)*n*(n+1)*(n+2)/15, n) for n>=1. - _Lechoslaw Ratajczak_, Feb 19 2017
%F A106616 From _Peter Bala_, Feb 24 2019: (Start)
%F A106616 a(n) = n/gcd(n,15), a quasi-polynomial in n since gcd(n,15) is a purely periodic sequence of period 15.
%F A106616 O.g.f.: F(x) - 2*F(x^3) - 4*F(x^5) + 8*F(x^15), where F(x) = x/(1 - x)^2.
%F A106616 O.g.f. for reciprocals: Sum_{n >= 1} x^n/a(n) = Sum_{d divides 15} (phi(d)/d) * log(1/(1 - x^d)) = log(1/(1 - x)) + (2/3)*log(1/(1 - x^3)) + (4/5)*log(1/(1 - x^5)) + (8/15)*log(1/(1 - x^15)), where phi(n) denotes the Euler totient function A000010. (End)
%F A106616 From _Amiram Eldar_, Nov 25 2022: (Start)
%F A106616 Multiplicative with a(3^e) = 3^max(0,e-1), a(5^e) = 5^max(0,e-1), and a(p^e) = p^e otherwise.
%F A106616 Sum_{k=1..n} a(k) ~ (49/150) * n^2. (End)
%p A106616 seq(numer(n/(n+15)),n=0..100); # _Nathaniel Johnston_, Apr 18 2011
%t A106616 f[n_]:=Numerator[n/(n+15)]; Array[f,100,0] (* _Vladimir Joseph Stephan Orlovsky_, Feb 17 2011*)
%o A106616 (Sage) [lcm(n,15)/15 for n in range(0, 79)] # _Zerinvary Lajos_, Jun 09 2009
%o A106616 (Magma) [Numerator(n/(n+15)): n in [0..100]]; // _Vincenzo Librandi_, Apr 18 2011
%o A106616 (PARI) a(n) = numerator(n/(n+15)); \\ _Michel Marcus_, Feb 19 2017
%o A106616 (GAP) List([0..80],n->NumeratorRat(n/(n+15))); # _Muniru A Asiru_, Feb 19 2019
%Y A106616 Cf. A000010, A106614, A106615, A106617, A106618, A106619, A106620, A106621.
%Y A106616 Cf. Other 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 A106616 nonn,easy,frac,mult
%O A106616 0,3
%A A106616 _N. J. A. Sloane_, May 15 2005