Is there a relation between number of divisors and ability to express a number as a perfect square.

Question

Is there a way to relate the number of ways of expressing an integer as a difference of squares to the number of divisors it has? Particularly, in the case of perfect squares.

Answer 1

For a number to be a perfect square, each prime factor appears with an even power.

Thus the total number of divisors are $$ (2k_1 +1)( 2k_2 +1)...(2k_n +1)$$ which is an odd integer.