Uva 11526 - H(n)

Analysis

According to the given code :: 

 long long H(int n){
long long res = 0;
for( int i = 1; i <= n; i=i+1 ){
res = (res + n/i);
}
return res;
}

We can get for n=20 is ::
20+10+6+5+4+3+2+2+2+2+1+1+1+1+1+1+1+1+1+1
=  20+10+6+5+4+3+8+10
=  20+10+6+5+10+8+4+3
=  20+10+6+5+1*(20-10)+2*(10-6)+3*(6-5)+4*(5-4)
=  20+10+6+5+20-10+20-12+18-15+20-16
=  20+10+6+5+20+10+6+5-16
= (20+10+6+5)+(20+10+6+5)-4*4
= 2(20+10+6+5) - 4*4

again, sqrt(20) = 4;

So, see that ...