Representations of integers as sums of powers with increasing exponents

Let(n) be the least integer such thatn may be represented in the formn=x₁²+x₂³+...+x_(n)⁽ⁿ⁾⁺¹ wherex₁,x₂, ...,x_(n) are natural numbers. We computed(n) forn 250 000 and found that(n) 5 for all thesen exceptn=56, 160 for which(n)=6. Also(n) 4 for 41542<n<=250 000.