A139329 Number of permutation symmetries of the 0s in the binary expansion of n. Consider the symmetric group that permutes floor(lg(n)) elements acting on the 0s.

1, 1, 1, 1, 2, 1, 1, 1, 6, 2, 2, 1, 2, 1, 1, 1, 24, 6, 6, 2, 6, 2