|
|
A109015
|
|
a(n) = gcd(n,12).
|
|
5
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).
|
|
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
|
|
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 *)
|
|
PROG
|
(Python)
from math import gcd
def a(n): return gcd(n, 12)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|