A109011 a(n) = gcd(n,8).

8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4

Offset: 0

Author

Mitch Harris

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A010877, A109004.

Programs

Mathematica

a[n_]:= GCD[n,8]; Array[a, 100, 0] (* Stefano Spezia, Nov 19 2018 *)

PARI

a(n) = gcd(n, 8) \\ David A. Corneth, Nov 19 2018

Formula

a(n) = 1 + [2|n] + 2*[4|n] + 4*[8|n], where [x|y] = 1 when x divides y, 0 otherwise.

a(n) = a(n-8).

Multiplicative with a(p^e) = gcd(p^e, 8). - David W. Wilson, Jun 12 2005

G.f.: ( -8 - x - 2*x^2 - x^3 - 4*x^4 - x^5 - 2*x^6 - x^7 ) / ( (x-1)*(1+x)*(x^2+1)*(x^4+1) ). - R. J. Mathar, Apr 04 2011

Dirichlet g.f.: zeta(s)*(1 + 1/2^s + 2/4^s + 4/8^s). - R. J. Mathar, Apr 04 2011

a(n) = 2^(-(101*m^7 - 2464*m^6 + 23786*m^ 5 -115360*m^4 + 293909*m^3 - 371056*m^2 + 186204*m - 15120)/5040) where m = (n mod 8). - Luce ETIENNE, Nov 18 2018