# Problem 448: Average least common multiple
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. Let
S(n)=∑A(k) for 1≤k≤n. S(100)=122726. Find S(99999999019) mod 999999017.