Sum of Squares
Consider equations of the form: a2 + b2 = N, 0 ≤ a ≤ b, a, b and N integer.
For N=65 there are two solutions:
a=1, b=8 and a=4, b=7.
We call S(N) the sum of the values of a of all solutions of a2 + b2 = N, 0 ≤ a ≤ b, a, b and N integer.
Thus S(65) = 1 + 4 = 5.
Find ∑S(N), for all squarefree N only divisible by primes of the form 4k+1 with 4k+1 < 150.