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%I #21 Oct 07 2023 05:06:40
%S 0,6,3,2,6,30,1,42,12,6,15,66,2,78,21,10,24,102,3,114,30,14,33,138,4,
%T 150,39,18,42,174,5,186,48,22,51,210,6,222,57,26,60,246,7,258,66,30,
%U 69,282,8,294,75,34,78,318,9,330,84,38,87,354,10,366,93,42
%N a(n) = lcm(n,6) / gcd(n,6).
%C If n == 2 or 4 (mod 6) then a(n) = 3*n/2; if n == 3 (mod 6) then a(n) = 2*n/3; if n == 1 or 5 (mod 6) then a(n) = 6*n; otherwise, a(n) = n/6. Examples: n = 50 = 6*8+2, a(50) = 3*50/2 = 75; n = 23 = 6*3+5, a(23) = 6*23 = 138. - _Bruno Berselli_, Mar 08 2017
%H Colin Barker, <a href="/A283443/b283443.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,2,0,0,0,0,0,-1).
%F G.f.: x*(6 + 3*x + 2*x^2 + 6*x^3 + 30*x^4 + x^5 + 30*x^6 + 6*x^7 + 2*x^8 + 3*x^9 + 6*x^10) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2).
%F a(n) = 2*a(n-6) - a(n-12) for n>11.
%F a(n) = A109047(n)/A089128(n). - _R. J. Mathar_, Feb 12 2019
%F Sum_{k=1..n} a(k) ~ (95/72)*n^2. - _Amiram Eldar_, Oct 07 2023
%t Table[LCM[n, 6] / GCD[n, 6], {n,0,63}] (* _Indranil Ghosh_, Mar 08 2017 *)
%o (PARI) concat(0, Vec(x*(6 + 3*x + 2*x^2 + 6*x^3 + 30*x^4 + x^5 + 30*x^6 + 6*x^7 + 2*x^8 + 3*x^9 + 6*x^10) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2) + O(x^100)))
%o (PARI) {for (n=0, 63, print1((lcm(n, 6) / gcd(n, 6)),", "))}; \\ _Indranil Ghosh_, Mar 08 2017
%Y Cf. A064680, A130724, A188134, A283442, A283444.
%K nonn,easy
%O 0,2
%A _Colin Barker_, Mar 07 2017