def add_carmichael_pfd(n):
Lsub_n.append(n)
this_n = len(Lsub_n)-1
Lsub_pfd.append([(2,1)])
#if (n+1) in primes_list:
if sum(1 for div in divisorGen(n+1))==2:
#first look if n+1 is prime, if yes add
Lsub_pfd[this_n].append((n+1,1))
if n in powers_of_2_list:
#also check if this new value is a power of 2
Lsub_pfd[this_n].append((2,2+int(math.log(n,2))))
#print Lsub_pfd
divisors_fcn = 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_fcn = []
a_list_fcn = []
for j in divisors_fcn:
if j!=1 and j!=n:
if j not in Lsub_n:
add_carmichael_pfd(j)
this_j = Lsub_n.index(j)
for p_a_fcn in Lsub_pfd[this_j]:
if len(p_a_fcn)>0:
if p_a_fcn[0] in p_list_fcn:
p_list_id_fcn = p_list_fcn.index(p_a_fcn[0])
a_list_fcn[p_list_id] = max(a_list_fcn[p_list_id_fcn],p_a_fcn[1])
else:
p_list_fcn.append(p_a_fcn[0])
a_list_fcn.append(p_a_fcn[1])
#print p_list_fcn
#print a_list_fcn
for j in xrange(len(p_list_fcn)):
if not p_list_fcn[j]==2:
#p=2 has a different formula
a_list_fcn[j] = max_pow( n / carmichael_1fact(p_list_fcn[j],a_list_fcn[j]) ,p_list_fcn[j]) + a_list_fcn[j]
else:
p_list.append(p_a[0])
a_list.append(p_a[1])
#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 not p_list[i]==2:
#p=2 has a different formula
a_list[i] = max_pow( n / carmichael_1fact(p_list[i],a_list[i]) ,p_list[i]) + a_list[i]
Lsub_list_next = Lsub_list_next * p_list[i]**a_list[i]
Lsub_list.append(Lsub_list_next)
#save the max_pfd
Lsub_pfd[n]=[]
for i in xrange(len(p_list)):
Lsub_pfd[n].append((p_list[i],a_list[i]))
if n%10000==0:
print '\n' + 'done ' + str(n) + ', ~' + "{0:.1%}".format(float(n)/float(total))
print len(str(max(Lsub_list)))
last_time = t5
t5 = time.time()
# 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))
elif n % 2 == 0:
a = 3
else:
a = 1
else:
a = max_pow(n / carmichael_1fact(p_list[i], 1), p_list[i]) + 1
Lsub_list_next = Lsub_list_next * p_list[i] ** a
if sum(1 for div in divisorGen(n + 1)) == 2:
Lsub_list_next = Lsub_list_next * (n + 1)
Lsub_list.append(Lsub_list_next)
if n % 10000 == 0:
print "\n" + "done " + str(n) + ", ~" + "{0:.1%}".format(float(n) / float(total))
print len(str(max(Lsub_list)))
last_time = t5
t5 = time.time()
print t5 - t3