A283443 a(n) = lcm(n,6) / gcd(n,6).

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, 150, 39, 18, 42, 174, 5, 186, 48, 22, 51, 210, 6, 222, 57, 26, 60, 246, 7, 258, 66, 30, 69, 282, 8, 294, 75, 34, 78, 318, 9, 330, 84, 38, 87, 354, 10, 366, 93, 42

Offset: 0

Author

Colin Barker, Mar 07 2017

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A064680, A130724, A188134, A283442, A283444.

Programs

Mathematica

Table[LCM[n, 6] / GCD[n, 6], {n,0,63}] (* Indranil Ghosh, Mar 08 2017 *)

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)))

PARI

{for (n=0, 63, print1((lcm(n, 6) / gcd(n, 6)),", "))}; \\ Indranil Ghosh, Mar 08 2017

Formula

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).

a(n) = 2*a(n-6) - a(n-12) for n>11.

a(n) = A109047(n)/A089128(n). - R. J. Mathar, Feb 12 2019

Sum_{k=1..n} a(k) ~ (95/72)*n^2. - Amiram Eldar, Oct 07 2023