$L_{loc}^{1}(\mathbb{R}^{n})\not\subset\mathcal{S}'(\mathbb{R}^{n})$

Question

I am looking for an example of a function $f \in L_{loc}^{1}(\mathbb{R}^{n})$ which does not induce a tempered distribution, where $L_{loc}^{1}(\mathbb{R}^{n}):= \{f $ measurable, $ \int_{K} \|f(x)\| < \infty $ for all compact $ K \subset \mathbb R^n \} $