A positive integer, $n$, is factorised into prime factors. We define $f(n)$ to be the product when each prime factor is replaced with $2$. In addition we define $f(1)=1$.

For example, $90=2\times 3\times 3\times 5$, then replacing the primes, $2\times 2\times 2\times 2=16$, hence $f(90)=16$.

Let ${\displaystyle S(N)=\sum _{n=1}^{N}f(n)}$. You are given $S({10}^8)=9613563919$.

Find $S({10}^{14})$.