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A283444 a(n) = lcm(n,7) / gcd(n,7).

%I A283444 #30 Oct 07 2023 05:06:44
%S A283444 0,7,14,21,28,35,42,1,56,63,70,77,84,91,2,105,112,119,126,133,140,3,
%T A283444 154,161,168,175,182,189,4,203,210,217,224,231,238,5,252,259,266,273,
%U A283444 280,287,6,301,308,315,322,329,336,7,350,357,364,371,378,385,8,399
%N A283444 a(n) = lcm(n,7) / gcd(n,7).
%C A283444 Similar to row 7 of A059897. Apart from the extra a(0) = 0, differs first at a(49) = 7 <> 343 = A059897(7,49). Note that a(1) = 7 also, whereas all rows of A059897 are permutations of the positive integers. - _Peter Munn_, Jan 16 2020
%H A283444 Colin Barker, <a href="/A283444/b283444.txt">Table of n, a(n) for n = 0..1000</a>
%H A283444 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,2,0,0,0,0,0,0,-1).
%F A283444 G.f.: x*(7 + 14*x + 21*x^2 + 28*x^3 + 35*x^4 + 42*x^5 + x^6 + 42*x^7 + 35*x^8 + 28*x^9 + 21*x^10 + 14*x^11 + 7*x^12) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^2).
%F A283444 a(n) = 2*a(n-7) - a(n-14) for n > 13.
%F A283444 a(n) = 7^(-(m^6 - 21*m^5 + 175*m^4 - 735*m^3 + 1624*m^2 - 1764*m + 360)/360)*n where m = (n mod 7). - _Luce ETIENNE_, Nov 18 2019
%F A283444 Sum_{k=1..n} a(k) ~ (295/98)*n^2. - _Amiram Eldar_, Oct 07 2023
%t A283444 Table[LCM[n, 7] / GCD[n, 7], {n,0,57}] (* _Indranil Ghosh_, Mar 08 2017 *)
%t A283444 LinearRecurrence[{0,0,0,0,0,0,2,0,0,0,0,0,0,-1},{0,7,14,21,28,35,42,1,56,63,70,77,84,91},60] (* _Harvey P. Dale_, Apr 05 2018 *)
%o A283444 (PARI) concat(0, Vec(x*(7 + 14*x + 21*x^2 + 28*x^3 + 35*x^4 + 42*x^5 + x^6 + 42*x^7 + 35*x^8 + 28*x^9 + 21*x^10 + 14*x^11 + 7*x^12) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)^2) + O(x^100)))
%o A283444 (PARI) {for (n=0, 57, print1((lcm(n, 7) / gcd(n, 7)),", "))}; \\ _Indranil Ghosh_, Mar 08 2017
%Y A283444 Cf. A059897, A064680, A130724, A188134, A283442, A283443.
%K A283444 nonn,easy
%O A283444 0,2
%A A283444 _Colin Barker_, Mar 07 2017