%I #13 Apr 30 2014 01:36:12
%S 1,2,1,3,2,1,4,2,3,1,5,2,2,4,1,6,3,2,2,5,1,7,2,3,3,2,6,1,8,4,2,2,2,3,
%T 7,1,9,2,3,4,4,2,2,8,1,10,5,3,2,2,2,3,4,9,1,11,2,2,3,5,5,3,2,2,10,1,
%U 12,6,4,3,2,2,2,2,3,5,11,1,13,2,3,4,2,6
%N Triangle T(n, k) where T(n, k) = T(k, n), T(n, n*k) = k, and T(n, n+k) = T(n, k) if k not divisible by n.
%C The function T(n, k) is defined for k>n but only the values for 1 <= k <= n as a triangular array are listed here.
%e {1}; {2, 1}; {3, 2, 1}; {4, 2, 3, 1}; {5, 2, 2, 4, 1}; {6, 3, 2, 2, 5, 1}; ...
%t T[ n_, k_] := If[ n < 1 || k < 1, 0, If[ Mod[n, k] == 0 || Mod[k, n] == 0, Max[n, k] / Min[n, k], T[ k, Mod[ n, k, 1]]]]
%o (PARI) {T(n, k) = if( n<1 || k<1, 0, if( n%k == 0 || k%n == 0, max(n, k) / min(n, k), T(k, (n-1)%k + 1)))}
%K nonn,tabl
%O 1,2
%A _Michael Somos_, Jul 20 2011