Unique Partition

\[ 5=1+4=2+3\] Let \(w(x) \) denote the number of ways to express a positive integer \(x\) as the sum of 1 or more positive integers, all of which are distinct.

For example, \(w(5) = 3,\) as shown above. Note that the order doesn't matter, so \((1+4) =(4+ 1)\) are considered the same thing.

Find the sum of all value of \(a>1\) such that \(w(a) = a \).

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