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]
print 'have ' + str(total+1) + ' lambda(p**1) values: ' + str(t3-t2)
#print lambda_list
t5 =t3
#begin Lsub_list at 0
Lsub_list = [0,2,24,2]
Lsub_pfd = [[],[(2,1)],[(2,3),(3,1)],[(2,1)]]
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]
#if not prime, attach (2,1) ... this saves us from using an "if statement" as we iterate below
Lsub_pfd.append([(2,1)])
#if (n+1) in primes_list:
if sum(1 for div in divisorGen(n+1)):
#first look if n+1 is prime, if yes add
Lsub_pfd[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[n].append((2,2+int(math.log(n,2))))
#print Lsub_pfd
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 = []
a_list = []
for i in divisors:
'''
Created on Nov 22, 2015
@author: Trader
'''
from PE003_Largest_Prime_Factor import divisorGen
a_list = []
#for i in range(11,28123+1):
for i in range(11,28123+1):
if 2*i < sum(divisorGen(i)):
a_list.append(i)
print 'done abundant list'
print len(a_list)
print max(a_list)
sum_list = []
for i in xrange(len(a_list)):
for j in xrange(i, len(a_list)):
if not i+j in sum_list:
sum_list.append(i+j)
print 'done the sum list'
print len(sum_list)
not_sum_list = []
for i in range(28123):
if not i in sum_list:
not_sum_list.append(i)
print sum(not_sum_list)
'''
Created on Nov 22, 2015
https://projecteuler.net/problem=21
@author: Trader
'''
from PE003_Largest_Prime_Factor import divisorGen
d_list=[0,1]
for i in range(2,10000+1):
d_list.append(sum(divisorGen(i))-i)
a_list = []
for i in range(2,10000+1):
if i not in a_list:
if i<>d_list[i]:
if d_list[i] <10001:
if d_list[d_list[i]]==i:
a_list.append(i)
a_list.append(d_list[i])
print a_list
print sum(a_list)