AoPS Wiki talk:Problem of the Day/August 8, 2011

We see that each coefficient of the terms of the polynomials is $1$, so we only need to determine how many terms $f$ has. We see that each term is of the form $x^n$, where $n$ is a perfect square. The largest of these $n$ is $n=1000000=100^2$, so the number of terms of $f$, and thus the sum of the coefficients of $f$, is $\boxed{100}$.