Unique Partition

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

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

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

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