A130724 a(n) = lcm(n,3) / gcd(n,3).

0, 3, 6, 1, 12, 15, 2, 21, 24, 3, 30, 33, 4, 39, 42, 5, 48, 51, 6, 57, 60, 7, 66, 69, 8, 75, 78, 9, 84, 87, 10, 93, 96, 11, 102, 105, 12, 111, 114, 13, 120, 123, 14, 129, 132, 15, 138, 141, 16, 147, 150, 17, 156, 159, 18, 165, 168, 19, 174, 177, 20, 183, 186

Offset: 0

Author

W. Neville Holmes, Jul 04 2007

Keywords

• easy
• nonn

Examples

			a(7) = 21 because lcm(3,7) = 21, gcd(3,7) = 1 and 21/1 = 21.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A109007, A109044.

Programs

Magma

[Lcm(n,3)/Gcd(n,3) : n in [0..100]]; // Wesley Ivan Hurt, Jul 24 2016

Maple

A130724:=n->lcm(n,3)/gcd(n,3): seq(A130724(n), n=0..100); # Wesley Ivan Hurt, Jul 24 2016

Mathematica

LCM[3,#]/GCD[3,#]&/@Range[0,70] (* Harvey P. Dale, May 16 2013 *)

Formula

a(n) = A109044(n) / A109007(n).

From Wesley Ivan Hurt, Jul 24 2016: (Start)

G.f.: x*(3 + 6*x + x^2 + 6*x^3 + 3*x^4)/(x^3 - 1)^2.

a(n) = 2*a(n-3) - a(n-6) for n>5.

a(n) = 27*n/(5 + 4*cos(2*n*Pi/3))^2.

If n mod 3 = 0, then n/3, else 3*n.

a(n) = lcm(numerator(n/3), denominator(n/3)). (End)

Sum_{k=1..n} a(k) ~ (19/18)*n^2. - Amiram Eldar, Oct 07 2023

Extensions

Corrected and extended by Harvey P. Dale, May 16 2013