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

An integer is called B-smooth if none of its prime factors is greater than $B$.

Let $S_B(n)$ be the largest $B$-smooth divisor of $n$.
Examples:
$S_1(10)=1$
$S_4(2100) = 12$
$S_{17}(2496144) = 5712$

Define $\\displaystyle F(n)=\\sum_{B=1}^n \\sum_{r=0}^n S_B(\\binom n r)$. Here, $\\displaystyle \\binom n r$ denotes the binomial coefficient.
Examples:
$F(11) = 3132$
$F(1111) \\mod 1\\,000\\,000\\,993 = 706036312$
$F(111\\,111) \\mod 1\\,000\\,000\\,993 = 22156169$

Find $F(11\\,111\\,111) \\mod 1\\,000\\,000\\,993$.

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