A109015 a(n) = gcd(n,12).

12, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2

Offset: 0

Author

Mitch Harris

Keywords

• nonn
• easy
• mult

Comments

Periodic, with period = 12. - Harvey P. Dale, Dec 20 2018

Links

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

Crossrefs

Cf. A109004.

Programs

Mathematica

GCD[Range[0,100],12] (* or *) PadRight[{},120,{12,1,2,3,4,1,6,1,4,3,2,1}] (* Harvey P. Dale, Dec 20 2018 *)

Python

from math import gcd
def a(n): return gcd(n, 12)
print([a(n) for n in range(99)]) # Michael S. Branicky, Dec 01 2021

Formula

a(n) = 1 + [2|n] + 2*[3|n] + 2*[4|n] + 2*[6|n] + 4*[12|n], where [x|y] = 1 when x divides y, 0 otherwise.

a(n) = a(n-12).

Multiplicative with a(p^e, 12) = gcd(p^e, 12). - David W. Wilson, Jun 12 2005

Dirichlet g.f.: zeta(s)*(1 + 1/2^s + 2/4^s)*(1 + 2/3^s). - R. J. Mathar, Apr 08 2011