Putnam 1961 A4

Let $\Omega(n)$ be the number of prime factors of $n$ . Define $f(1)=1$ and $f(n)=(-1)^{\Omega(n)}.$ Furthermore, let $$F(n)=\sum_{d|n} f(d).$$ Prove that $F(n)=0,1$ for all positive integers $n$ . For which integers $n$ is $F(n)=1?$