a^2 + b^3 + c^4 + d^5...

[Don Reble]

> the number of ways in which an integer can be expressed as the sum of
> integers (>1) to different powers (>1).

> it looks like 291 is the largest integer which cannot be expressed as
> such a sum. Is 291 the largest such integer? 

Well, it's the largest below 2^24.
In case you want a confirmation, I find that these are unrepresentable:

1 2 3 5 6 7 10 11 13 14 15 18 19 21 22 23 26 29 30 34 35 37 38 39 42 45
46 50 51 53 54 55 58 61 62 66 67 69 70 71 74 77 78 82 83 86 87 94 99 101
102 103 109 110 115 118 119 126 131 135 142 147 151 158 163 167 179 183
195 199 211 227 291

-- 
Don Reble  djr at nk.ca