Arithmetic function: Difference between revisions

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In [[number theory]], an '''arithmetic function''' (or '''number-theoretic function''') ''f''(''n'') is a [[function]] defined for all positive [[integer|integers]] and having values in the [[complex number|complex numbers]]. The(''f'' most: important'''N''' arithmetic<font functionssize=+1 arecolor=darkgreen> the&rarr; [[multiplicative</font> function|multiplicative]]'''C'''). ones.

Another definition of arithmetic function is a function with properties:

:&Psi;(''m''+''n'') = &Psi;[&Psi;(''m'')+&Psi;(''n'')]

:&Psi;(''m'',''n'') = &Psi;[&Psi;(''m'')&Psi;(''n'')]

The most important arithmetic functions are the [[multiplicative function|multiplicative]] ones.

Arithmetic function should not be confused with a function sometimes called ''arithmetical function''.