A070292 a(n) = lcm(12,n)/gcd(12,n).

12, 6, 4, 3, 60, 2, 84, 6, 12, 30, 132, 1, 156, 42, 20, 12, 204, 6, 228, 15, 28, 66, 276, 2, 300, 78, 36, 21, 348, 10, 372, 24, 44, 102, 420, 3, 444, 114, 52, 30, 492, 14, 516, 33, 60, 138, 564, 4, 588, 150, 68, 39, 636, 18, 660, 42, 76, 174, 708, 5, 732, 186, 84, 48

Offset: 1

Author

Amarnath Murthy, May 10 2002

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A070290, A070291, A070293, A109015, A109053.

Programs

PARI

for(n=1,100,print1(lcm(12,n)/gcd(n,12),","))

PARI

Vec(x*(12 + 6*x + 4*x^2 + 3*x^3 + 60*x^4 + 2*x^5 + 84*x^6 + 6*x^7 + 12*x^8 + 30*x^9 + 132*x^10 + x^11 + 132*x^12 + 30*x^13 + 12*x^14 + 6*x^15 + 84*x^16 + 2*x^17 + 60*x^18 + 3*x^19 + 4*x^20 + 6*x^21 + 12*x^22) / (x^24 - 2*x^12 + 1) + O(x^60)) \\ Colin Barker, Mar 05 2019

Python

from math import gcd, lcm
def a(n): return lcm(12, n)//gcd(12, n)
print([a(n) for n in range(1, 65)]) # Michael S. Branicky, Dec 06 2021

Formula

a(n) = A109053(n)/A109015(n) = 12*n/A109015(n)^2. - R. J. Mathar, Feb 12 2019

a(n) = 2*a(n-12) - a(n-24). - R. J. Mathar, Feb 12 2019

G.f.: x*(12 + 6*x + 4*x^2 + 3*x^3 + 60*x^4 + 2*x^5 + 84*x^6 + 6*x^7 + 12*x^8 + 30*x^9 + 132*x^10 + x^11 + 132*x^12 + 30*x^13 + 12*x^14 + 6*x^15 + 84*x^16 + 2*x^17 + 60*x^18 + 3*x^19 + 4*x^20 + 6*x^21 + 12*x^22) / (x^24 - 2*x^12 + 1). - Colin Barker, Mar 05 2019

Sum_{k=1..n} a(k) ~ (703/288)*n^2. - Amiram Eldar, Oct 07 2023

Extensions

More terms from Benoit Cloitre, May 16 2002