[Math] abelian groups of order $10^5$

Question

I was trying to solve the following problem:

Find number of abelian groups of order $10^5$, up to isomorphism ?
Could someone point me in the right direction?

Thanks in advance for your time.

Answer 1

Hint : The number of abelian groups of order $$p_1^{a_1}\cdots p_n^{a_n}$$

upto isomorphism is $$p(a_1)\cdots p(a_n)$$ where $p(n)$ denotes the number of partitions of $n$