A109013 a(n) = gcd(n,10).

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, 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, 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

Offset: 0

Author

Mitch Harris

Keywords

• nonn
• easy
• mult

Crossrefs

Cf. A109004.

Programs

Mathematica

GCD[Range[0,100],10] (* Harvey P. Dale, Jul 11 2011 *)

Formula

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

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

Multiplicative with a(p^e, 10) = gcd(p^e, 10). - David W. Wilson, Jun 12 2005

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

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

a(n) = ((n-1) mod 2 + 1)*(4*floor(((n-1) mod 5)/4) + 1). - Gary Detlefs, Dec 28 2011