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

[Dr. Gordon Hamilton]

I've just submitted a sequence which counts the number of ways in which an 
integer can be expressed as the sum of integers (>1) to different powers 
(>1).  For example:

F(292) = 17 because:

292 = 14^2 + 4^3 + 2^5
292 = 14^2 + 2^5 + 2^6
292 = 13^2 + 3^3 + 2^5 + 2^6
292 = 11^2 + 3^3 + 2^4 + 2^7
292 = 10^2 + 4^3 + 2^7
292 = 10^2 + 2^6 + 2^7
292 = 7^2 + 3^5
292 = 6^2 + 4^3 + 2^6 + 2^7
292 = 6^2 + 4^4
292 = 6^2 + 2^8
292 = 5^2 + 3^3 + 2^4 + 2^5 + 2^6 + 2^7
292 = 5^2 + 2^3 + 2^4 + 3^5
292 = 3^2 + 3^3 + 4^4
292 = 3^2 + 3^3 + 2^8
292 = 2^2 + 4^3 + 2^5 + 2^6 + 2^7
292 = 2^2 + 4^4 + 2^5
292 = 2^2 + 2^5 + 2^8

My program is not very efficient so I've only checked to 1500, but so far it 
looks like 291 is the largest integer which cannot be expressed as such a 
sum. Is 291 the largest such integer?