Representing a big number

The ways to represent $n=p_1^{k_1}...p_r^{k_r}$ as a product of $\delta$ factors is

$\rho_\delta (n)=\displaystyle\prod_{k_i=\upsilon_p(n)}\binom{k_i+\delta-1}{k_i}$

So when $\delta=3$ our answer is 28.28= $\boxed{784}$ .

Note :If someone could tell me if there actually is such a function $\rho_\delta(n)$ , please tell me, because I have found it by myself while solving problems such as this one.

although i got it right the below mentiond way...i found a problem that is

4 4 k and 4 4 k will be added in the combinations..where k is sutable number