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A109044 a(n) = lcm(n,3).

%I A109044 #47 Sep 08 2023 07:33:25
%S A109044 0,3,6,3,12,15,6,21,24,9,30,33,12,39,42,15,48,51,18,57,60,21,66,69,24,
%T A109044 75,78,27,84,87,30,93,96,33,102,105,36,111,114,39,120,123,42,129,132,
%U A109044 45,138,141,48,147,150,51,156,159,54,165,168,57,174,177,60,183,186,63
%N A109044 a(n) = lcm(n,3).
%H A109044 G. C. Greubel, <a href="/A109044/b109044.txt">Table of n, a(n) for n = 0..1000</a>
%H A109044 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%H A109044 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>.
%F A109044 a(n) = 3*n/gcd(n,3) = 3*n/A109007(n).
%F A109044 From _Bruno Berselli_, Mar 11 2011: (Start)
%F A109044 G.f.: 3*x*(1+2*x+x^2+2*x^3+x^4)/(1-x^3)^2.
%F A109044 a(n) = 3*A051176(n);
%F A109044 a(n) = n*(7-2*A099837(n))/3 for n>0. (End)
%F A109044 From _Wesley Ivan Hurt_, Jul 24 2016: (Start)
%F A109044 a(n) = 2*a(n-3) - a(n-6) for n>5.
%F A109044 a(n) = 9*n/(5 + 4*cos(2*n*Pi/3)).
%F A109044 If n mod 3 = 0 then 3*floor(n/3), else 3*n. (End)
%F A109044 a(n) = n*(1 + 2*((n^2) mod 3)). - _Timothy Hopper_, Feb 23 2017
%F A109044 From _Michael Somos_, Mar 04 2017: (Start)
%F A109044 G.f.: 3 * x / (1 - x)^2 - 6 * x^3 / (1 - x^3)^2. -
%F A109044 a(n) = a(-n) for all n in Z. (End)
%F A109044 Sum_{k=1..n} a(k) ~ (7/6) * n^2. - _Amiram Eldar_, Nov 26 2022
%F A109044 Sum_{n>=1} (-1)^(n+1)/a(n) = 5*log(2)/9. - _Amiram Eldar_, Sep 08 2023
%e A109044 G.f. = 3*x + 6*x^2 + 3*x^3 + 12*x^4 + 15*x^5 + 6*x^6 + 21*x^7 + 24*x^8 + ...
%p A109044 A109044:=n->lcm(n,3): seq(A109044(n), n=0..100); # _Wesley Ivan Hurt_, Jul 24 2016
%t A109044 LCM[Range[0, 100], 3] (* _Wesley Ivan Hurt_, Jul 24 2016 *)
%o A109044 (Sage) [lcm(n,3)for n in range(0, 64)] # _Zerinvary Lajos_, Jun 07 2009
%o A109044 (Magma) [Lcm(n,3): n in [0..63]]; // _Bruno Berselli_, Mar 11 2011
%o A109044 (PARI) a(n)=lcm(n,3) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A109044 Cf. A051176, A099837, A109007 (gcd(n,3)), A109042.
%K A109044 nonn,easy
%O A109044 0,2
%A A109044 _Mitch Harris_, Jun 18 2005