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

Let $SB(n)$ be the largest B-smooth divisor of $n$.

Examples:

$$\begin{align} & S_1(10) = 1 \\ & S_4(2\,100) = 12 \\ & S_{17}(2\,496\,144) = 5\,712 \end{align}$$

Define $F(n) = \displaystyle\sum_{B = 1}^n \sum_{r = 0}^n S_B(\displaystyle\binom{n}{r})$. Here, $\displaystyle\binom{n}{r}$ denotes the binomial coefficient.

Examples:

$$\begin{align} & F(11) = 3132 \\ & F(1\,111)\bmod 1\,000\,000\,993 = 706\,036\,312 \\ & F(111\,111)\bmod 1\,000\,000\,993 = 22\,156\,169 \end{align}$$

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

--hints--

smoothDivisorsOfBinomialCoefficients() should return 852950321.

assert.strictEqual(smoothDivisorsOfBinomialCoefficients(), 852950321);

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function smoothDivisorsOfBinomialCoefficients() {

  return true;
}

smoothDivisorsOfBinomialCoefficients();

--solutions--

// solution required