First Chebyshev function
This article is about a function defined on positive reals (and in particular, natural numbers) obtained as the summatory function of an arithmetic function.
View other such summations
Let be a positive real number. The first Chebyshev function of , denoted or , is defined as:
where the sum is only over the prime numbers less than or equal to .
Relation with other counting functions
- Prime-counting function: Denoted , this simply counts the number of primes less than or equal to .
- Second Chebyshev function: A similar summation, but this time of the von Mangoldt function over all prime powers less than or equal to .