All Questions
1
question
1
vote
2
answers
367
views
Logarithm of factorial equal to sum of logarithm of primes
Let $N$ a positive integer. Denote $\mathcal{P}$ the set of prime numbers. I have to show that
\begin{align}
\log(N!) = \sum_{p^{\nu}\leq N \\ p\in \mathcal{P}} \left\lfloor\dfrac{N}{p^{\nu}}\right\...
- 866