{"app":{"locale":"en-GB"},"problem":{"content":"

Define f_k(n) = $\\sum_{i=0}^{n}$ f_k($\\lfloor\\frac{i}{k}\\rfloor$) where f_k(0) = 1 and $\\lfloor x \\rfloor$ denotes the floor function.

For example, f₅(10) = 18, f₇(100) = 1003, and f₂(10³) = 264830889564.

Find $(\\sum_{k=2}^{10}$ f_k(10¹⁴)$)$ mod (10⁹+7).

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