Arithmetic function: Difference between revisions
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In [[number theory]], an '''arithmetic function''' is a function defined on the set of [[postive integers]], usually with integer, [[real number|real]] or [[complex number|complex]] values. | In [[number theory]], an '''arithmetic function''' is a function defined on the set of [[postive integers]], usually with integer, [[real number|real]] or [[complex number|complex]] values. | ||
Revision as of 14:55, 9 November 2008
In number theory, an arithmetic function is a function defined on the set of postive integers, usually with integer, real or complex values.
Classes of arithmetic function
Arithmetic functions which have some connexion with the additive or multiplicative structure of the integers are of particular interest in number theory. We define a function a(n) on positive integers to be
- Totally multiplicative if for all m and n.
- Multiplicative if whenever m and n are coprime.
