it is well known that there exist numbers that are the sum of their digits to some fixed power: 153 = 1^3 + 5^3 + 3^3 4151 = 4^5 + 1^5 + 5^5 + 1^5 consider instead the problem of expressing a number as the sum of its digits to different powers, similar to david wilson's recent post on energetic numbers. we would like to make the minimum m of those powers is as large as possible. for example, here is an example where the smallest power is m=7: 3212 = 3^7 + 2^9 + 1^9 + 2^9 it seems like there should be no upper bound on possible values for m, but i have not been able to find any larger than m=7. can any of you? erich