## Smooth divisors of binomial coefficients

Published on Saturday, 19th April 2014, 01:00 pm; Solved by 202;
Difficulty rating: 70%

### Problem 468

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:
S1(10) = 1
S4(2100) = 12
S17(2496144) = 5712

Define F(n) = ∑1≤Bn0≤rn SB(C(n,r)). Here, C(n,r) denotes the binomial coefficient.
Examples:
F(11) = 3132
F(1 111) 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.