## Average least common multiple

### Problem 448

Published on Sunday, 24th November 2013, 01:00 am; Solved by 172; Difficulty rating: 80%
The function **lcm**(a,b) denotes the least common multiple of a and b.

Let A(n) be the average of the values of lcm(n,i) for 1≤i≤n.

E.g: A(2)=(2+2)/2=2 and A(10)=(10+10+30+20+10+30+70+40+90+10)/10=32.

S(100)=122726.

Find S(99999999019) mod 999999017.