Let set  $S=\{a_1,a_2,a_3,\dots ,a_{12}\}$  where all twelve elements are distinct, we want to form sets  each of which contains one or more of the elements of set  $S$  (including the possibility of  using all the elements of S). The only restriction is that the subscript of each element in a  specific set must be an integral multiple of the smallest subscript in the set. For example,  $\{a_2,a_6,a_8\}$   is one acceptable set. Number of such sets can be formed, is K. Where sum of the digits K is …..