A143525 a(n) = the number of divisors of (A005179(n)-1), where A005179(n) is the smallest positive integer with n divisors.

1, 2, 2, 4, 2, 6, 2, 4, 2, 8, 2, 24, 2, 4, 4, 16, 2, 32, 2, 6, 4, 16, 2, 8, 4, 4, 4, 64, 2, 96, 2, 8, 4, 4, 2, 512, 2, 4, 4, 192, 2, 144, 2, 4, 6, 16, 4, 16, 8, 8, 8, 128, 2, 12, 2, 16, 4, 64, 2, 4608, 4, 12, 2, 12, 8, 384, 4, 8, 2, 512, 2, 8192, 16, 4, 16, 8, 8, 192, 4, 8, 4, 32, 4, 24, 8