Arithmetic Function - Notation

Notation

and mean that the sum or product is over all prime numbers:

Similarly, and mean that the sum or product is over all prime powers with strictly positive exponent (so 1 is not counted):

and mean that the sum or product is over all positive divisors of n, including 1 and n. E.g., if n = 12,

The notations can be combined: and mean that the sum or product is over all prime divisors of n. E.g., if n = 18,

and similarly and mean that the sum or product is over all prime powers dividing n. E.g., if n = 24,