I got pretty good results with complexity of O(sqrt(N)).
if (N == 1) return 1;
int divisors = 0;
int max = N;
for (int div = 1; div < max; div++) {
if (N % div == 0) {
divisors++;
if (div != N/div) {
divisors++;
}
}
if (N/div < max) {
max = N/div;
}
}
return divisors;