13.5 It is known that a set of 6 weights can be used to measure 63 objects of consecutive natural number weights using a balance scale. Find this set of weights.
［Solution］Since the partial sums of the weights of the weights can be consecutive natural numbers, there must be a weight of 1 among them, and the first 3 weights should be $1,2,4$. Thus, the 4th weight does not exceed 8, the 5th does not exceed 16, and the 6th does not exceed 32. If the 6th weight is less than 32, then it is impossible to measure 63, so the weights of the 6 weights are $1,2,4,8,16,32$.