PotD3.py

# improve A(n)
# H(n) improves by working from both sides in at the same time

def A(n):
    res = 0
    for i in range(1,n+1):
       res += n // i
    return res

def H(n):
    if (n == 1):
        return 1
    i = 1
    val = n
    count = 0
    while (i < val):
        val = n//i
        count += val + i * (val - n//(i + 1))  #second portion sums all i's that would appear later
        i += 1
    if (i != val):
        count -= val
    return count