# Prime Number Related Notation Question

1. Oct 12, 2011

### kenzidelx

Is there any standard (or reasonably standard) notation for the following function?

Basically, it's

∏(n) - ∏(n-1)

or, which is the same thing,

$\frac{\Lambda(n)}{\log n}$

(where ∏(n) is the Riemann prime counting function and $\Lambda$(n) is the Von Mangoldt function)

Basically, it's the function that is 1/a if n = p^a, where p is some prime, and 0 otherwise.

I use it all the time, and writing $\frac{\Lambda(n)}{\log n}$ for it is pretty unwieldy. Actually, while on the topic, does it have any sort of standard name?