A379496 a(n) = A019565(1+n) - A019565(A001065(n)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.
2, 4, 3, 4, 13, 15, 5, -16, 16, 35, 33, 59, 103, 189, -3, -188, 31, -44, 53, -55, 123, 225, 75, 89, 216, 451, 315, 385, 1153, 2037, 11, -2284, -171, 23, -5, -4160, 193, 225, 69, -247, 271, -1599, 453, 819, 1339, 2499, 141, -309, 422, 312, 605, 65, 2143, 4239, 979, 1985, 2673, 5993, 5003, 2275, 15013, 29991, -165
Offset: 1