Arithmetic functions vs. Sequences What is the difference between arithmetic functions and sequences? The definition looks similar though for both. I got confused when this term was introduced in the class of 'Analytic Number Theory'. Please help me understand this. Thanks in advance.
 A: In some sense there's no difference, but in practice when you call something an arithmetic function as opposed to a sequence you are paying attention to the multiplicative structure of $\mathbb{N}$ and the examples you care about will be attuned to that multiplicative structure. Examples include the totient function $\varphi(n)$, the divisor function $d(n)$, etc. This is particularly clear in the definition of a multiplicative arithmetic function, which is one satisfying
$$f(mn) = f(m) f(n)$$
where $\gcd(m, n) = 1$. 
There are a few other places in mathematics where people use different names for the same thing and the goal is to activate different kinds of context. For example, quivers are just a certain kind of graph (specifically, directed multigraphs, or "multidigraphs" if you really want), but they're not called graphs because they're not studied by graph theorists; instead they're studied by algebraists, who ask very different questions about them than the kinds of questions graph theorists ask about graphs. So the choice to use "quiver" instead of "directed multigraph" is a choice to activate this algebraic context and not a graph-theoretic context.
Similarly, the choice to use "arithmetic function" instead of "sequence" is a choice to activate a number-theoretic context. 
