A078882 Number of subsets S of {1,2,3,...,n} with the largest possible cardinality consistent with the requirement that if i and j are distinct elements of S then i XOR j is not in S. XOR is the bitwise exclusive-OR operator.

1, 1, 3, 3, 1, 3, 7, 7, 3, 1, 1, 1, 3, 7, 15, 15, 7, 3, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 7, 15, 31, 31, 15