mult = lambda_list[0]
for i in range (1,len(lambda_list)):
mult = lcm(mult,lambda_list[i])
return mult
total=20000000
t0 = time.time()
#get all primes first
#primes_list = list(primes(total+1))
t1 = time.time()
#print 'have sub-' + str(total+1) + ' primes: ' + str(t1-t0)
#print primes_list
powers_of_2_list = list(powers_of_2(total))
print len(powers_of_2_list)
t2 = time.time()
print 'have sub-' + str(total+1) + ' powers of 2: ' + str(t2-t1)
#have one lambda list, shared by all calculations for Lsub
#initialize the list with lambda(p**a) for a=1
#where we need lambda(p**a) for a>1, we will add these values as needed
#lambda_list = []
#for i in primes_list:
#lambda_list.append([carmichael_1fact(i,1)])
#lambda_list.append(carmichael_1fact(i,1))
t3 = time.time()
print 'have ' + str(total+1) + ' lambda(p**1) values: ' + str(t3-t2)
#print lambda_list
t5 =t3
############ FIRST PASS to 1 million
#########################################################################################
#########################################################################################
#########################################################################################
#########################################################################################
true_total = 20000000
total=1000000
t0 = time.time()
#get all primes first
#primes_list = list(primes(total+1))
t1 = time.time()
#print 'have sub-' + str(total+1) + ' primes: ' + str(t1-t0)
#print primes_list
powers_of_2_list = list(powers_of_2(true_total))
#print len(powers_of_2_list)
t2 = time.time()
print 'have sub-' + str(total+1) + ' powers of 2: ' + str(t2-t1)
#have one lambda list, shared by all calculations for Lsub
#initialize the list with lambda(p**a) for a=1
#where we need lambda(p**a) for a>1, we will add these values as needed
#lambda_list = []
#for i in primes_list:
#lambda_list.append([carmichael_1fact(i,1)])
#lambda_list.append(carmichael_1fact(i,1))
t3 = time.time()
print 'have ' + str(total+1) + ' lambda(p**1) values: ' + str(t3-t2)
#print lambda_list
t5 =t3