import math

def maxPrimeFactor(n):
    p = 2
    while (p <= n/p):
        if (n%p):
            p += 1
        else:
            n/=p
    return n

def gcd(a,b):
    c = 1
    while (b):
        c = b
        b = a % b
        a = c
    return a

def sn(n):
    solution = prod = 1
    p = maxPrimeFactor(n)
    pFac = math.factorial(p)
    if((pFac%n) == 0 and pFac>=n):
        solution = p
    else:
        rest = n / gcd(pFac, n)
        solution = p+1
        prod = p + 1
        while(prod < rest):
            solution += 1
            prod *= solution
        while (prod % rest):
            solution += 1
            prod *= solution
    return solution

sum = 0
for i in range(2,100000001):
    sum += sn(i)
print sum

f(p * m) = g(f(p), f(m))

def _s_for_prime_power(n,p):
    k=0
    while p > n:
        k += n
        p -= n + 1
        t=k
        while t%n!=0:
            t=t//n
            p-=1
    return (k + max(0,p)) * n;