def main(): # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # print primes.getPrimeFactors(4) # print primes.getPrimeFactors(6) # print primes.getPrimeFactors(59) # print primes.getPrimeFactors(13195) print primes.getPrimeFactors(600851475143)[-1]
def findNumsWithDumbReduction():
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
reducible_num = []
reducible_den = []
for den in xrange(11, 100):
if den%10 == 0:
continue
for num in xrange(11, den):
if num%10 == 0:
continue
reduced = doDumbReduction(num, den)
red_frac = float(reduced['num'])/reduced['den']
if float(num)/den == red_frac:
reducible_num.append(reduced['num'])
reducible_den.append(reduced['den'])
print 'reduced nums: %s' % reducible_num
print 'reduced denoms: %s' % reducible_den
red_product_num = reduce(operator.mul, reducible_num)
red_product_den = reduce(operator.mul, reducible_den)
print 'product of reduced nums: %d' % red_product_num
print 'product of reduced denoms: %d' % red_product_den
print 'product of reduced fracs: %f' % (float(red_product_num)/red_product_den)
primes_list = primes.primeSeive(red_product_num)
print primes_list
prime_factors_num = collections.Counter( primes.getPrimeFactors( red_product_num
, primes_list)
)
prime_factors_den = collections.Counter( primes.getPrimeFactors( red_product_den
, primes_list)
)
common_prime_factors = list((prime_factors_num & prime_factors_den).elements())
for p in common_prime_factors:
red_product_num /= p
red_product_den /= p
print 'Fully reduced product of special fractions is %d/%d = %f' % ( red_product_num
, red_product_den
, ( float(red_product_num)/red_product_den)
)
def sumOfDivisors(num, primes_list):
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
if num == 0 or num == 1:
return 0
prime_factors = collections.Counter(primes.getPrimeFactors(num, primes_list))
sum_of_divisors = 1
for pf in prime_factors:
temp = 0
for i in xrange(prime_factors[pf] + 1):
temp += pf ** i
sum_of_divisors *= temp
return sum_of_divisors - num