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 A106615 #47 May 27 2025 01:07:12
%S A106615 0,1,1,3,2,5,3,1,4,9,5,11,6,13,1,15,8,17,9,19,10,3,11,23,12,25,13,27,
%T A106615 2,29,15,31,16,33,17,5,18,37,19,39,20,41,3,43,22,45,23,47,24,7,25,51,
%U A106615 26,53,27,55,4,57,29,59,30,61,31,9,32,65,33,67,34,69,5,71,36,73,37,75,38,11,39
%N A106615 a(n) = numerator of n/(n+14).
%C A106615 A multiplicative function and also 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 22 2019
%H A106615 Nathaniel Johnston, <a href="/A106615/b106615.txt">Table of n, a(n) for n = 0..10000</a>
%H A106615 Wikipedia, <a href="https://en.wikipedia.org/wiki/Quasi-polynomial">Quasi-polynomial</a>.
%H A106615 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (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,-1).
%F A106615 Dirichlet g.f.: zeta(s-1)*(1 - 6/7^s - 1/2^s + 6/14^s). - _R. J. Mathar_, Apr 18 2011
%F A106615 a(n) = 2*a(n-14) - a(n-28). - _G. C. Greubel_, Feb 19 2019
%F A106615 From _Peter Bala_, Feb 22 2019: (Start)
%F A106615 a(n) = n/gcd(n,14).
%F A106615 a(n) = n/b(n), where b(n) = [1, 2, 1, 2, 1, 2, 7, 2, 1, 2, 1, 2, 1, 14, ...] is a purely periodic sequence of period 14. Thus a(n) is a quasi-polynomial in n.
%F A106615 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 A106615 O.g.f.: Sum_{d divides 14} A023900(d)*x^d/(1 - x^d)^2 = x/(1 - x)^2 - x^2/(1 - x^2)^2 - 6*x^7/(1 - x^7)^2 + 6*x^14/(1 - x^14)^2.
%F A106615 O.g.f. for reciprocals: Sum_{n >= 1} (1/a(n))*x^n = L(x) + 1/2*L(x^2) + 6/7*L(x^7) + 6/14*L(x^14), where L(x) = log (1/(1 - x)). (End)
%F A106615 From _Amiram Eldar_, Nov 25 2022: (Start)
%F A106615 Multiplicative with a(2^e) = 2^max(0,e-1), a(7^e) = 7^max(0,e-1), and a(p^e) = p^e otherwise.
%F A106615 Sum_{k=1..n} a(k) ~ (129/392) * n^2. (End)
%p A106615 seq(numer(n/(n+14)),n=0..100); # _Nathaniel Johnston_, Apr 18 2011
%t A106615 f[n_]:=Numerator[n/(n+14)];Array[f,100,0] (* _Vladimir Joseph Stephan Orlovsky_, Feb 17 2011 *)
%o A106615 (Sage) [lcm(n,14)/14 for n in range(0, 100)] # _Zerinvary Lajos_, Jun 09 2009
%o A106615 (Magma) [Numerator(n/(n+14)): n in [0..100]]; // _Vincenzo Librandi_, Apr 18 2011
%o A106615 (PARI) vector(100, n, n--; numerator(n/(n+14))) \\ _G. C. Greubel_, Feb 19 2019
%o A106615 (GAP) List([0..80],n->NumeratorRat(n/(n+14))); # _Muniru A Asiru_, Feb 19 2019
%Y A106615 Cf. A023900, A106614, A106616, A106621.
%Y A106615 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 A106615 nonn,easy,frac,mult
%O A106615 0,4
%A A106615 _N. J. A. Sloane_, May 15 2005