Show that $\sum_{k\leq n} \Omega(k) = \sum_{p\leq n} \alpha_{n!}(p)$

2018-02-13 05:27:12

How to show that $\sum_{k\leq n} \Omega(k) = \sum_{p\leq n} \alpha_{n!}(p)$, the sum of the exponents in the prime factorization of $n!$