%I #26 Oct 19 2019 03:20:32

%S 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,

%T 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,

%U 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

%N a(n) = gcd(n,7).

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1).

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

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

%F Multiplicative with a(p^e, 7) = gcd(p^e, 7). - _David W. Wilson_, Jun 12 2005

%F From _R. J. Mathar_, Apr 04 2011: (Start)

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

%F 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)

%F a(n) = 6*floor(((n-1) mod 7)/6) + 1. - _Gary Detlefs_, Dec 28 2011

%p A109010:=n->gcd(n,7): seq(A109010(n), n=0..150); # _Wesley Ivan Hurt_, Apr 27 2017

%t GCD[Range[0,100],7] (* or *) PadRight[{},120,{7,1,1,1,1,1,1}] (* _Harvey P. Dale_, Apr 26 2018 *)

%Y Cf. A109004.

%K nonn,easy,mult

%O 0,1

%A _Mitch Harris_