A161789 a(n) = the largest integer k such that {2^k -1} divides n.

1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 3, 4, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 3, 1, 4, 5, 1, 2, 1, 3, 2, 1, 1, 2, 1, 1, 3, 1, 1, 4, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 4, 1, 5, 6, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 4, 1, 3, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 4, 3, 1, 5, 1, 1, 2, 1, 3, 2, 1, 1, 2, 1, 1, 4