# Problem 580: Squarefree Hilbert numbers
A Hilbert number is any positive integer of the form \$4k+1\$ for
integer \$k\\geq 0\$. We shall define a squarefree Hilbert number as a
Hilbert number which is not divisible by the square of any Hilbert
number other than one. For example, \$117\$ is a squarefree Hilbert
number, equaling \$9\\times13\$. However \$6237\$ is a Hilbert number
that is not squarefree in this sense, as it is divisible by \$9\^2\$.
The number \$3969\$ is also not squarefree, as it is divisible by both
\$9\^2\$ and \$21\^2\$. There are \$2327192\$ squarefree Hilbert numbers
below \$10\^7\$. How many squarefree Hilbert numbers are there below
\$10\^{16}\$?