A unit fraction is a fraction of the form 1/n where n is a positive integer. Note that the unit unifraction 1/11 can be written as the sum of two unit fractions in the following three ways:

1/11=1/12+1/132=1/22+1/22=1/132+1/12

Are there any other ways of decomposing 1/11 into the sum of two unit fractions? In how many ways can we write 1/60 as the sum of two unit fractions? More generally, in how many ways can the unit fraction 1/n be written as the sum of two unit fractions?

In other words, how many ordered pairs (a, b) of positive integers a, b are there for which 1/n=1/a+1/b?