Marinada '22

[lang=hr] Kruna Slavomirove kolekcije ipak je jedan zadatak koji je vidio još dok nije znao reći ni kosinus (Je li to izvor njegovih čudnih zanimacija? Tko bi znao...) \\Neka je $f(x)=(x^2+3x+2)^{\cos(\pi x)}$. Pronađi zbroj svih prirodnih brojeva $n$ za koje je $\left |\sum_{k=1}^n\log_{10}f(k)\right|=1.$ [/lang] [lang=en] Crown jewel of Slavomir's collection is a problem that he saw long time ago, when he couldn't yet even spell cos (Might this be the source of his strange hobby? Who's to say...)\\ Let $f(x)=(x^2+3x+2)^{\cos(\pi x)}$. Find the sum of all positive integers $n$ for which $\left |\sum_{k=1}^n\log_{10}f(k)\right|=1$ holds true. [/lang]