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a(n) = gcd(n,10).
6

%I #22 Oct 18 2019 03:59:25

%S 10,1,2,1,2,5,2,1,2,1,10,1,2,1,2,5,2,1,2,1,10,1,2,1,2,5,2,1,2,1,10,1,

%T 2,1,2,5,2,1,2,1,10,1,2,1,2,5,2,1,2,1,10,1,2,1,2,5,2,1,2,1,10,1,2,1,2,

%U 5,2,1,2,1,10,1,2,1,2,5,2,1,2,1,10,1,2,1,2,5,2,1,2,1,10,1,2,1,2,5,2,1

%N a(n) = gcd(n,10).

%F a(n) = 1 + [2|n] + 4*[5|n] + 4*[10|n], where [x|y] = 1 when x divides y, 0 otherwise.

%F a(n) = a(n-10).

%F Multiplicative with a(p^e, 10) = gcd(p^e, 10). - _David W. Wilson_, Jun 12 2005

%F G.f.: ( -10 - x - 2*x^2 - x^3 - 2*x^4 - 5*x^5 - 2*x^6 - x^7 - 2*x^8 - x^9 ) / ( (x-1)*(1+x)*(x^4 + x^3 + x^2 + x + 1)*(x^4 - x^3 + x^2 - x+1) ). - _R. J. Mathar_, Apr 04 2011

%F Dirichlet g.f.: zeta(s)*(1 + 1/2^s + 4/5^s + 4/10^s). - _R. J. Mathar_, Apr 04 2011

%F a(n) = ((n-1) mod 2 + 1)*(4*floor(((n-1) mod 5)/4) + 1). - _Gary Detlefs_, Dec 28 2011

%t GCD[Range[0,100],10] (* _Harvey P. Dale_, Jul 11 2011 *)

%Y Cf. A109004.

%K nonn,easy,mult

%O 0,1

%A _Mitch Harris_