A099311 Exponent of greatest power of 2 dividing the smallest number having exactly n divisors.

0, 1, 2, 1, 4, 2, 6, 3, 2, 4, 10, 2, 12, 6, 4, 3, 16, 2, 18, 4, 6, 10, 22, 3, 4, 12, 2, 6, 28, 4, 30, 3, 10, 16, 6, 2, 36, 18, 12, 4, 40, 6, 42, 10, 4, 22, 46, 3, 6, 4, 16, 12, 52, 2, 10, 6, 18, 28, 58, 4, 60, 30, 6, 3, 12, 10, 66, 16, 22, 6, 70, 5, 72, 36, 4, 18, 10, 12, 78, 4, 2, 40, 82, 6, 16