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Smallest prime factor

Published on Sunday, 21st June 2015, 01:00 am; Solved by 573;
Difficulty rating: 45%

Problem 521

Let smpf(n) be the smallest prime factor of n.
smpf(91)=7 because 91=7×13 and smpf(45)=3 because 45=3×3×5.
Let S(n) be the sum of smpf(i) for 2 ≤ i ≤ n.
E.g. S(100)=1257.

Find S(1012) mod 109.