Question 90
A quadruple $(a, b, c, d)$ of positive integers is called *green* if
$$
b = a^2 + 1, \quad c = b^2 + 1, \quad d = c^2 + 1
$$
holds, and $D(a) + D(b) + D(c) + D(d)$ is odd, where $D(k)$ denotes the number of positive divisors of $k$.
How many green quadruples having elements less than 1 000 000 are there?
$$
b = a^2 + 1, \quad c = b^2 + 1, \quad d = c^2 + 1
$$
holds, and $D(a) + D(b) + D(c) + D(d)$ is odd, where $D(k)$ denotes the number of positive divisors of $k$.
How many green quadruples having elements less than 1 000 000 are there?