Prime divisor count function
From Number
This article defines an arithmetic function or number-theoretic function: a function from the natural numbers to a ring (usually, the ring of integers, rational numbers, real numbers, or complex numbers).
View a complete list of arithmetic functions
Definition
Let be a natural number. The prime divisor count function of
, denoted
, is defined as the number of prime divisors of
.
Relation with other arithmetic functions
- Mobius function: This is defined as
for
a square-free number, and is
otherwise.
- Divisor count function: This is denoted
, and is defined as the total number of positive divisors of
.
- Largest prime power divisor: Denoted
, this is defined as the largest prime power dividing
. We have:
.