Are equal power sum sets (EPSS) for second power, but the sum 4+5+12 is not the smallest. Find the smallest with all distinct positive integers.

Find EPSS of four numbers each (8 distinct positive integers) where the first, second and third powers have equal sums.

Keep going, if possible, to find higher order EPSS where fourth, fifth powers, etc. have equal sums.

Note: The highest EPSS I have is fifth power.