A165924 a(n) = number of square-full non-zero quadratic residues of n.

0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 2, 2, 4, 3, 3, 3, 4, 5, 6, 4, 4, 5, 4, 5, 7, 5, 8, 4, 6, 7, 4, 5, 8, 8, 7, 7, 10, 7, 7, 7, 6, 11, 12, 5, 9, 8, 7, 9, 11, 10, 9, 10, 10, 12, 12, 9, 14, 15, 8, 6, 9, 12, 12, 11, 14, 11, 20, 10, 17, 14, 9, 13, 10, 13, 18, 8, 12, 17, 17, 11, 12, 17