A283442 - OEIS

%I #21 Nov 17 2024 15:56:46

%S 0,5,10,15,20,1,30,35,40,45,2,55,60,65,70,3,80,85,90,95,4,105,110,115,

%T 120,5,130,135,140,145,6,155,160,165,170,7,180,185,190,195,8,205,210,

%U 215,220,9,230,235,240,245,10,255,260,265,270,11,280,285,290

%N a(n) = lcm(n,5) / gcd(n,5).

%H Colin Barker, <a href="/A283442/b283442.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,0,-1).

%F G.f.: x*(5 + 10*x + 15*x^2 + 20*x^3 + x^4 + 20*x^5 + 15*x^6 + 10*x^7 + 5*x^8) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2).

%F a(n) = A109046(n) / A109009(n).

%F a(n) = 2*a(n-5) - a(n-10) for n>9.

%F Sum_{k=1..n} a(k) ~ (101/50)*n^2. - _Amiram Eldar_, Oct 07 2023

%t Table[LCM[n, 5] / GCD[n, 5], {n,0,58}] (* _Indranil Ghosh_, Mar 08 2017 *)

%t LinearRecurrence[{0,0,0,0,2,0,0,0,0,-1},{0,5,10,15,20,1,30,35,40,45},60] (* _Harvey P. Dale_, Aug 11 2019 *)

%o (PARI) concat(0, Vec(x*(5 + 10*x + 15*x^2 + 20*x^3 + x^4 + 20*x^5 + 15*x^6 + 10*x^7 + 5*x^8) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2) + O(x^100)))

%o (PARI) {for (n=0, 58, print1((lcm(n, 5) / gcd(n, 5)),", "))}; \\ _Indranil Ghosh_, Mar 08 2017

%Y Cf. A064680, A130724, A188134, A283443, A283444.

%Y Cf. A109009, A109046.

%K nonn,easy

%O 0,2

%A _Colin Barker_, Mar 07 2017