Perfect Power Divisors

For a positive integer $m$, let's define a function $f(m)$ as the sum of all perfect powers which divide $m$. We call a positive integer $k$ a perfect power if there are integers $x$ and $y$ such that $k = x^y$ and $y \gt 1$. You need to calculate the sum $f(1) + f(2) + \ldots + f(N)$. Since the answer might be quite big, compute it modulo $1,000,000,007$ ($10^9 + 7$). ### Input - The first