A109010 a(n) = gcd(n,7).

7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1

Offset: 0

Author

Mitch Harris

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A109004.

Programs

Maple

A109010:=n->gcd(n,7): seq(A109010(n), n=0..150); # Wesley Ivan Hurt, Apr 27 2017

Mathematica

GCD[Range[0,100],7] (* or *) PadRight[{},120,{7,1,1,1,1,1,1}] (* Harvey P. Dale, Apr 26 2018 *)

Formula

a(n) = 1 + 6*[7|n], where [x|y] = 1 when x divides y, 0 otherwise.

a(n) = a(n-7).

Multiplicative with a(p^e, 7) = gcd(p^e, 7). - David W. Wilson, Jun 12 2005

From R. J. Mathar, Apr 04 2011: (Start)

Dirichlet g.f.: zeta(s)*(1 + 6/7^s).

G.f.: (-7 - x - x^2 - x^3 - x^4 - x^5 - x^6) / ((x-1)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). (End)

a(n) = 6*floor(((n-1) mod 7)/6) + 1. - Gary Detlefs, Dec 28 2011