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Let $f$ be an arithmetical function. Suppose that $f(n)>0$ if $n$ is in an integer set $A$ and that $f(n)<0$ for another integer set $B.$ Is there a result from number theory or an elementary ...

I was wondering if there exists or can we construct (using known arithmetic functions) an arithmetical function that has the same behaviour of the function sine or comparable to it (I mean that ...