freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-468-smooth-divisors-of-binomial-coefficients.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f5411000cf542c510054	Problem 468: Smooth divisors of binomial coefficients	5	302143	problem-468-smooth-divisors-of-binomial-coefficients

--description--

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);

--seed--

--seed-contents--

function smoothDivisorsOfBinomialCoefficients() {

  return true;
}

smoothDivisorsOfBinomialCoefficients();

--solutions--

// solution required