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Algebra Level 5

Let f(x)=(x2+3x+2)cos(πx)f(x)=(x^2+3x+2)^{\cos(\pi x)}. Find the sum of all positive integers nn for which k=1nlog10f(k)=1.\left |\displaystyle\sum_{k=1}^n\log_{10}f(k)\right|=1.

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