import time
from primes import divisors, factor, pfactor_gen
START = time.time()
SIZE = 10**6
factors = pfactor_gen(SIZE)
for i in xrange(2,SIZE,2):
if sum(divisors(i)) % i == i/2:
print i, factor(i)
print "Time Taken:", time.time() - START
"""
2: 1,3,7,15,31,65,129
3: 1,4,10,40,121,364
5: 1,6,31,156,781,3906
p(2) = 3/2 -> 1 1/2
p(24) = (13 * 4)/8 = 6 1/2
p(4320) = (63 * 40 * 6) = 3 1/2
-> 2^4 * 3^3 * 5 * 7
4320 = 2^5 * 3^3 * 5
2 [2]
24 [2, 2, 2, 3]
4320 [2, 2, 2, 2, 2, 3, 3, 3, 5]
4680 [2, 2, 2, 3, 3, 5, 13]
import time, string
from primes import pfactor_gen, factor_given_pfactor
from itertools import combinations
START = time.time()
SIZE = 10**8
pfactor = pfactor_gen(SIZE)
primes = [2, 3, 5, 7, 11, 13, 17, 19]
def factor(n):
return factor_given_pfactor(n, pfactor)
def mapToFactorPow(n):
factors = factor(n)
powCounts = [factors.count(x) for x in set(factors)]
return tuple(sorted(powCounts)[::-1])
def getMaxOptions(distro):
lettersMerged = string.join([str(i) * num for i, num in enumerate(distro)],
'')
return len(set( combinations( \
lettersMerged, \
len(lettersMerged)/2 )))
gmo = getMaxOptions
possible = dict()
#NOTE TODO need to solve it
import time
from primes import pfactor_gen, factor_given_pfactor, get_divisors_given_pfactor
START = time.time()
SIZE = 10**6
pfactor = pfactor_gen(SIZE)
def factor(n):
return factor_given_pfactor(n, pfactor)
def get_divisors(n):
return get_divisors_given_pfactor(n, pfactor)
# This function is currently very slow for numbers with lots of factors =/
def practical_check(n):
divs = get_divisors(n)
div_sums = set([0])
for val in divs:
div_sums.update(set([ val + num for num in div_sums]))
div_sums = sorted(div_sums)[:n+1]
print "On item:", n, "Time up to now:", time.time() - START
return div_sums == range(n+1)
pc = practical_check
items = []
for i in xrange(21,SIZE-18,2):
if pfactor[i] == i and pfactor[i+6] == i+6 and \
pfactor[i+12] == i+12 and pfactor[i+18] == i+18:
import time, math
from primes import get_primes, factor_given_pfactor, pfactor_gen, get_divisors_given_pfactor
START = time.time()
SIZE = 10**8
primesList = get_primes(SIZE)
pfactorList = pfactor_gen(SIZE)
primeSet = set(primesList)
def factor(n):
return factor_given_pfactor(n, pfactorList)
def divisors(n):
return get_divisors_given_pfactor(n, pfactorList)
answers = set()
for p in primesList:
print p
divs = divisors(p + 1)
for div1 in divs:
for div2 in divs:
if div1 <= div2:
continue
top = ((p + 1) * div1) / div2 - 1
bottom = ((p + 1) * div2) / div1 - 1
if top > SIZE:
continue
if top in primeSet and bottom in primeSet:
START = time.time()
SIZE = 10**6
def get_divisors(n): # returns all divisors of n.
return get_divisors_given_pfactor(n, pfactors)
def factor(n):
return sorted(factor_given_pfactor(n, pfactors))
def rep_dig_prime(p):
potential_pows = get_divisors(p-1)
for powz in potential_pows:
if pow(10,powz,p) == 1:
return powz
pfactors = pfactor_gen(SIZE)
values = [0] * SIZE
values[3] = 1
for i in xrange(5,SIZE,2): #Evens are easy to compute, do it later
if i %1024 == 1:
print i
if i %5 == 0: # multiples of 5 add no extra digits from the factor of 5.
values[i] = values[i/5]
continue
if pfactors[i] == i:
values[i] = rep_dig_prime(i)
else:
prime_factors = factor(i)
values[i] = 1
for (index,prime) in enumerate(prime_factors):
if prime == 3 and index == 1:
import time, math
from primes import get_primes, factor_given_pfactor, pfactor_gen, get_divisors_given_pfactor
START = time.time()
SIZE = 10**8
primesList = get_primes(SIZE)
pfactorList = pfactor_gen(SIZE)
primeSet = set(primesList)
def factor(n):
return factor_given_pfactor(n, pfactorList)
def divisors(n):
return get_divisors_given_pfactor(n, pfactorList)
answers = set()
for p in primesList:
print p
divs = divisors(p+1)
for div1 in divs:
for div2 in divs:
if div1 <= div2:
continue
top = ((p+1) * div1) / div2 - 1
bottom = ((p+1) * div2) / div1 - 1
if top > SIZE:
continue
if top in primeSet and bottom in primeSet:
answers.add((top, p, bottom))
print sum([x[0] +x[1] + x[2] for x in answers])