f=lambda n,k=2:n<k or f(n,k+1)-f(n/k)
import sys
sys.setrecursionlimit(20000)
for n in range(1, 11) + [117, 5525, 7044, 8888, 10000]:
print '%5d -> %3d' % (n, f(n))
Standard input is empty
    1 ->   1
    2 ->   0
    3 ->  -1
    4 ->  -1
    5 ->  -2
    6 ->  -1
    7 ->  -2
    8 ->  -2
    9 ->  -2
   10 ->  -1
  117 ->  -5
 5525 ->   5
 7044 -> -25
 8888 ->   4
10000 -> -23