For every integer n>1, the family of functions f_n,a,b is defined by f_n,a,b(x)≡ax+b mod n for a,b,x integer and 0<a<n, 0≤b<n, 0≤x<n.
We will call f_n,a,b a retraction if f_n,a,b(f_n,a,b(x))≡f_n,a,b(x) mod n for every 0≤x<n.
Let R(n) be the number of retractions for n.

You are given that
∑ R(c) for c=C(100 000,k), and 1 ≤ k ≤99 999 ≡628701600 (mod 1 000 000 007).
(C(n,k) is the binomial coefficient).

Find ∑ R(c) for c=C(10 000 000,k), and 1 ≤k≤ 9 999 999.
Give your answer modulo 1 000 000 007.