##Javascript (ES6), 53 bytes
n=>{for(i=2,r=0;i<n;n%i?i++:r+=!((n/=i)%i));return r}
Example:
let e =
n=>{for(i=2,r=0;i<n;n%i?i++:r+=!((n/=i)%i));return r}
// computing e(n) for n in [1, 30]
for(var n = 1, list = []; n <= 30; n++) {
list.push(e(n));
}
console.log(list.join(','));