A113594 - OEIS

%I #24 Apr 08 2023 04:51:18

%S 1,1,1,1,2,2,1,3,4,4,2,2,8,8,1,1,6,12,4,16,20,20,2,2,4,8,8,16,40,40,1,

%T 1,2,2,6,12,12,12,32,64,16,80,20,100,120,120,2,2,4,4,4,8,8,8,16,16,16,

%U 32,40,200,240,240,1,1,2,2,2,4,6,6,12,12,24,24,12,12,72,144,32,64,192,384

%N a(1) = a(2) = 1; a(n+1) = GCD(Sum_{1<=k<=n/2} a(k), Sum_{n/2<j<=n} a(j)).

%C a(2n-1) divides a(2n), for every positive integer n.

%H John Tyler Rascoe, <a href="/A113594/b113594.txt">Table of n, a(n) for n = 1..10000</a>

%e a(12) = GCD(a(1)+a(2)+a(3)+a(4)+a(5), a(6)+a(7)+a(8)+a(9)+a(10)+a(11)) = GCD(1+1+1+1+2, 2+1+3+4+4+2) = GCD(6,16) = 2.

%t a[1] = a[2] = 1; a[n_] := a[n] = GCD[ Sum[a[k], {k, Floor[(n - 1)/2]}], Sum[a[j], {j, Ceiling[n/2], n - 1}]]; Array[a, 82] (* _Robert G. Wilson v_, Feb 01 2006 *)

%o (Python)

%o from math import gcd

%o def A113594_list(nmax):

%o     A = [1,1]

%o     x,y = A[0],A[1]

%o     for n in range(3,nmax+1):

%o         z = (n-2)//2

%o         if n%2 != 0 and n > 4:

%o             x += A[z]

%o             y -= A[z]

%o         A.append(gcd(x,y))

%o         y += A[-1]

%o     return A # _John Tyler Rascoe_, Apr 07 2023

%K nonn

%O 1,5

%A _Leroy Quet_, Jan 26 2006

%E More terms from _Robert G. Wilson v_, Feb 01 2006