For the divisor function $\sigma_k(n)=\sum_{d|n}d^k$, is there any definition for $\sigma_k(0)$?

Question

For the divisor function $$\sigma_k(n)=\sum_{d|n}d^k$$ is there any definition for $\sigma_k(0)$?

The reason why I am asking is because I want ot calculate $E_4^2$ , $$E_4=1+240\sum_{n=1}^{\infty}\sigma_3(n)q^n $$ using the cauchy product .