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Smooth divisors of binomial coefficients

Problem 468

Published on 19 April 2014 at 01:00 pm [Server Time]

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≤B≤n ∑0≤r≤n 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.


Answer:
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