Revision as of 02:34, 29 April 2009 by Vipul
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
Let be a natural number. The square-free kernel or square-free part of is the product of all the prime divisors of .
Relation with other arithmetic functions
This arithmetic function is a multiplicative function: the product of this function for two natural numbers that are relatively prime is the value of the function at the product.
View a complete list of multiplicative functions
Preservation of divisibility
This arithmetic function is a divisibility-preserving function: if one natural number divides another, the value of the function at the first number also divides the value at the second number.
View other divisibility-preserving functions