Additive function

Completely additive

Examples

• The restriction of the logarithmic function to N.
• The multiplicity of a prime factor p in n, that is the largest exponent m for which p^m divides n.
• a₀ - the sum of primes dividing n counting multiplicity, sometimes called sopfr, the potency of n or the integer logarithm of n. For example:
• The function Ω, defined as the total number of prime factors of n, counting multiple factors multiple times, sometimes called the "Big Omega function". For example;

• ω, defined as the total number of different prime factors of n. For example:
• a₁ - the sum of the distinct primes dividing n, sometimes called sopf. For example:

  Multiplicative functions

Summatory functions