Maximal Unity

Let S_N be the set of positive numbers less or equal to N. For example S₅={1,2,3,4,5} Find the subset of S₁₀₀ with maximal number of elements (MN) such that sum(1/e_i)=1 for i=1 to MN and the sum T=sum(i*e_i) for i=1 to MN is maximal. Answer format: MN,T Example: 3,26 For the subset S={e₁=2, e₂=3, e₃=6} of S₆