def resilience_complex(d):
fd = [x for (x,y) in factorize(d)] # Factors of d.
r = d - 1
for sss in range(1,len(fd)+1): # subset size
sign = ((-1) ** sss)
for c in itertools.combinations(fd,sss):
prod = 1
for f in c :
prod *= f
r += sign*((d-1)/prod)
return (1.0*r/(d-1))
sign = ((-1) ** sss)
for c in itertools.combinations(fd,sss):
prod = 1
for f in c :
prod *= f
r += sign*((d-1)/prod)
return (1.0*r/(d-1))
resilience = resilience_complex
assert (resilience(12) == (4.0/11))
assert (resilience(509) == 1)
n = 2*3*5*7*11*13*17
#assert(resilience_simple(n) == resilience_complex(n))
#print n, resilience(n)
#exit(0)
# Safe to assume that d must be a multiple of all the small primes.
d = n
minr = 1
while True:
d += n
r = resilience(d)
minr = min(r,minr)
print minr, d, r
if (r < (15499.0/94744)):
print "****", d, "****"
print "****(", [x for x in factorize(d)], ")****"
break
