In fact, only using integers between 2 and 45 inclusive, there are exactly three ways to do it, the remaining two being: {2,3,4,6,7,9,10,20,28,35,36,45} and {2,3,4,6,7,9,12,15,28,30,35,36,45}.
How many ways are there to write the number $\frac{1}{2}$ as a sum of inverse squares using distinct integers between 2 and 80 inclusive?