ILL 1976 Problem 42

For a point $O$ inside a triangle $ABC$ , denote by $A_1,B_1, C_1,$ the respective intersection points of $AO, BO, CO$ with the corresponding sides. Let $$n_1 =\frac{AO}{A_1O}, n_2 = \frac{BO}{B_1O}, n_3 = \frac{CO}{C_1O}.$$ What possible values of $n_1, n_2, n_3$ can all be positive integers?