A283442 a(n) = lcm(n,5) / gcd(n,5).

0, 5, 10, 15, 20, 1, 30, 35, 40, 45, 2, 55, 60, 65, 70, 3, 80, 85, 90, 95, 4, 105, 110, 115, 120, 5, 130, 135, 140, 145, 6, 155, 160, 165, 170, 7, 180, 185, 190, 195, 8, 205, 210, 215, 220, 9, 230, 235, 240, 245, 10, 255, 260, 265, 270, 11, 280, 285, 290

Offset: 0

Author

Colin Barker, Mar 07 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).

Crossrefs

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

Cf. A109009, A109046.

Programs

Mathematica

Table[LCM[n, 5] / GCD[n, 5], {n,0,58}] (* Indranil Ghosh, Mar 08 2017 *)
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 *)

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)))

PARI

{for (n=0, 58, print1((lcm(n, 5) / gcd(n, 5)),", "))}; \\ Indranil Ghosh, Mar 08 2017

Formula

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).

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

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

Sum_{k=1..n} a(k) ~ (101/50)*n^2. - Amiram Eldar, Oct 07 2023