SP11202 NUMTRY - Number Theory

f(n) and g(n) are two functions defined as following : f(n) = ∏( p $ _{i} $ $ ^{2ei+1} $ +1 ), where p $ _{i} $ is prime factor of n and e $ _{i} $ is highest power of p $ _{i} $ in n. g(n) = Σ( n/gcd(n,i) ); 1

First line has T (

\[f(n)/g(n)\] % 1000000007 for each test case.