In number theory, an arithmetic, arithmetical, or number-theoretic function is a real or complex valued function $f(n)$ defined on the set of natural numbers (i.e. positive integers) that "expresses some arithmetical property of $n$."
To emphasize that they are being thought of as functions rather than sequences, values of an arithmetic function are usually denoted by $a(n)$ rather than $a_n$.
There is a larger class of number-theoretic functions that do not fit the above definition, e.g. the prime-counting functions.