def totient(x):
t = x
for (k,l) in factorGen(x):
t -= t // k
return t
'''
n_list_mult = [2,3,5,7,11,13]
n_list_mult = [1]
for i in n_list_mult:
n_list.append(i*2*3*5*7*11*13)
'''
#for i in xrange(len(p_list)):
for n in n_list:
#looking for a fraction less than 15499/94744
#once we find the fraction, look for the true lowest denom in the range
all_p_list = list(primes(n))
#get divisors for prod
div_list = [a for (a,b) in factorGen(n)]
#print div_list
#create list of resilient fractions based on primes (to the power of 1 only):
#does not include divisors of n
#must be less than n
p_list = []
for p in all_p_list:
if p >= n: break
if not p in div_list:
p_list.append(p)
all_list=[]
new_list = p_list
while len(new_list)>0:
last_list = new_list
for n in range(4, total + 1):
# for each calculation of L_sub[n], iterate through all divisors of n
# for each divisor, get the prime factor decomposition (pfd) st. L_sub[divisor] = p1**a1 * .. * pn**an
# for each prime, p get the max value a, s.t. a = max(a_divisor1, ..., a_divisor_n)
# if n+1 is prime, then include (n+1)**1 in the pdf for L_sub[n]
divisors = list(divisorGen(n))
# aggregate the prime fact decomps of the max_pfd for each divisor
# merge like primes by keeping the max value for a
p_list = []
for i in divisors:
if i != 1 and i != n:
print i, Lsub_list[i]
for p_a in factorGen(Lsub_list[i]):
if not p_a[0] in p_list:
p_list.append(p_a[0])
# print p_list
# print a_list
# check if any primes further divide n
# also we calc Lsub[n] by iteratively multiplying by p**a as we determine the max power for a
Lsub_list_next = 1
for i in xrange(len(p_list)):
# we know p**a divides n
# check if p**(a+1) divides n
# or just find b s.t. p**b divides (n/ p**a), so then max power is a+b
if p_list[i] == 2:
if n % 4 == 0:
a = 2 + int(math.log(n, 2))
