For every integer $n>1$, the family of functions $f_{n,a,b}$ is defined by
$f_{n,a,b}(x)\equiv ax+b\mathrm{mod}n$ for $a,b,x$ integer and $0<a<n,0\le b<n,0\le x<n$.

We will call $f_{n,a,b}$ a retraction if $f_{n,a,b}(f_{n,a,b}(x))\equiv f_{n,a,b}(x)\mathrm{mod}n$ for every $0\le x<n$.
Let $R(n)$ be the number of retractions for $n$.

${\displaystyle F(N)=\sum _{n=1}^{N}R(n^4+4)}$.
$F(1024)=77532377300600$.

Find $F({10}^7)$.
Give your answer modulo $1000000007$.