Scary function and spooky summation!

Calculus Level 5

\[\large \left|\displaystyle\sum_{k=1}^n \log_{10} f(k)\right|=1\]

Let \(\large f(x)=(x^2+3x+2)^{\cos(\pi x)}\). Find the product of all positive integers \(n\) satisfying the equation above.

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