import math
def prime(n):
primes=[]
h  = [True] * int(n+1)
h[:2] = [False, False]
for i in range(2, int(n ** (1.0*0.5)) + 1):
if h[i]:
h[i*i::i] = [False] * len(h[i*i::i])
for i, e in enumerate(h):
if e:
primes.append(i)
return primes

def S(n):
p=prime(n//2)
m=[1]* int(n+1)
L=len(p)
for x1 in range(0,L):
if p[x1]*p[x1]>n:break
for a1 in range(1,1+int(math.log(n,p[x1]))):
t1=p[x1]**a1
if t1>n:break
m[t1]=a1
for x2 in range(x1+1,L):
if p[x2]>n/t1:break
for a2 in range(1,1+int(math.log(n,p[x2]))):
t2=t1*p[x2]**a2
if t2>n:break
m[t2]=a1+a2
for x3 in range(x2+1,L):
if p[x3]>n/t2:break
for a3 in range(1,1+int(math.log(n,p[x3]))):
t3=t2*p[x3]**a3
if t3>n:break
m[t3]=a1+a2+a3
for x4 in range(x3+1,L):
if p[x4]>n/t3:break
for a4 in range(1,1+int(math.log(n,p[x4]))):
t4=t3*p[x4]**a4
if t4>n:break
m[t4]=a1+a2+a3+a4
for x5 in range(x4+1,L):
if p[x5]>n/t4:break
for a5 in range(1,1+int(math.log(n,p[x5]))):
t5=t4*p[x5]**a5
if t5>n:break
m[t5]=a1+a2+a3+a4+a5
for x6 in range(x5+1,L):
if p[x6]>n/t5:break
for a6 in range(1,1+int(math.log(n,p[x6]))):
t6=t5*p[x6]**a6
if t6>n:break
m[t6]=a1+a2+a3+a4+a5+a6
for x7 in range(x6+1,L):
if p[x7]>n/t6:break
for a7 in range(1,1+int(math.log(n,p[x7]))):
t7=t6*p[x7]**a7
if t7>n:break
m[t7]=a1+a2+a3+a4+a5+a6+a7
for x8 in range(x7+1,L):
if p[x8]>n/t7:break
for a8 in range(1,1+int(math.log(n,p[x8]))):
t8=t7*p[x8]**a8
if t8>n:break
m[t8]=a1+a2+a3+a4+a5+a6+a7+a8
#print(m)
s=0
for i in m:
s+=2**i
print(s-2-1)

import time
t=time.time()
S(10**8)
print(time.time()-t)

>>>> import time
>>>> t=time.time()
>>>> S(10**8)
9613563919
>>>> print(time.time()-t)
42.9400000572