%I #31 Nov 26 2022 04:03:36

%S 0,12,12,12,12,60,12,84,24,36,60,132,12,156,84,60,48,204,36,228,60,84,

%T 132,276,24,300,156,108,84,348,60,372,96,132,204,420,36,444,228,156,

%U 120,492,84,516,132,180,276,564,48,588,300,204,156,636,108,660,168

%N a(n) = lcm(n,12).

%H Muniru A Asiru, <a href="/A109053/b109053.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,-1).

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>.

%F a(n) = n*12/gcd(n, 12).

%F a(n) = 12*A051724(n). - _R. J. Mathar_, Feb 12 2019

%F From _Colin Barker_, Mar 04 2019: (Start)

%F G.f.: 12*x*(1 + x + x^2 + x^3 + 5*x^4 + x^5 + 7*x^6 + 2*x^7 + 3*x^8 + 5*x^9 + 11*x^10 + x^11 + 11*x^12 + 5*x^13 + 3*x^14 + 2*x^15 + 7*x^16 + x^17 + 5*x^18 + x^19 + x^20 + x^21 + x^22) / (1 - 2*x^12 + x^24).

%F a(n) = 2*a(n-12) - a(n-24) for n>23.

%F (End)

%F Sum_{k=1..n} a(k) ~ (77/24) * n^2. - _Amiram Eldar_, Nov 26 2022

%t Array[LCM[#,12]&,60,0] (* _Harvey P. Dale_, Mar 26 2015 *)

%o (Sage) [lcm(n,12) for n in range(0,57)] # _Zerinvary Lajos_, Jun 09 2009

%o (GAP) List([0..60],n->Lcm(n,12)); # _Muniru A Asiru_, Mar 04 2019

%o (PARI) concat(0, Vec(12*x*(1 + x + x^2 + x^3 + 5*x^4 + x^5 + 7*x^6 + 2*x^7 + 3*x^8 + 5*x^9 + 11*x^10 + x^11 + 11*x^12 + 5*x^13 + 3*x^14 + 2*x^15 + 7*x^16 + x^17 + 5*x^18 + x^19 + x^20 + x^21 + x^22) / (1 - 2*x^12 + x^24) + O(x^40))) \\ _Colin Barker_, Mar 04 2019

%o (PARI) for(n=0,60, print1(lcm(n,12), ", ")) \\ _G. C. Greubel_, Mar 06 2019

%o (Magma) [LCM(n, 12): n in [0..60]]; // _G. C. Greubel_, Mar 06 2019

%Y Cf. A051724, A109042.

%K nonn,easy

%O 0,2

%A _Mitch Harris_, Jun 18 2005