The problem is: write 101! in canonical form.
I solved it by try to find the highest power of each factor prime factor less than 101. When running factor()
function using TI-89, I realized that the power of each prime factor decrease. So I guess I have two questions:
- How can write this idea using Math notation? I'm think of $\prod$ and $\sum$ notation, but I don't know how to express this idea.
- As a programmer, I want to write a program to handle this situation. I could check every prime factor, however, I'm curious about the decrease of these prime factor. Is there any pattern behind the scene? If there is, it would increase my algorithm a bit.
Update
Based on Aryabhata's answer, my attempt is: $\prod_{i=1}^{\infty}p_i^{\sum_{k=1}^{\infty} \left\lfloor\frac{n}{p^k}\right\rfloor}$
Does it make sense?
Thanks.