Continuous, Differentiable Function with Certain Properties

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Let $f(n,x)$ be a continuous, differentiable function that the number of terms does not depend on $n$ (aka $\sum$, $\prod$, etc.) $f(n,x)=0$ only when $n/x$ is an integer ($x$ need not to be an integer). These properties only have to hold for $-n\leq x \leq n$ What is an example of such $f(n,x)$?