Smallest prime factor

 Published on Sunday, 21st June 2015, 01:00 am; Solved by 681;
Difficulty rating: 50%

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 ≤ in.
E.g. S(100)=1257.

Find S(1012) mod 109.