def findFactorsPairs(N):
factors = []
bound = (N // 2) + 1
norig = N
checkup = N / 5
for k in sieveEratosthenes(bound):
j = 0
while N % k == 0:
j += 1
N = N // k
if j > 0:
factors.append((k,j))
if N == 1:
break
if len(factors) == 0:
factors.append(N)
assert lu.product(factors) == norig, (str(factors) + (", %d != %d" % (lu.product(factors), norig)))
return factors
def factorTrialDivision(N,primeList=None,verbose=False):
factors = []
if primeList == None:
bound = (N // 2) + 1
primeList = sieveEratosthenes(bound)
norig = N # Original N for latter verification
i = 0
checkup = N / 5
for k in primeList:
while N % k == 0:
factors.append(k)
N = N // k
if N == 1:
break
if verbose and i % (checkup) == 0:
print "%d..." % k
i = i+1
if len(factors) == 0:
factors.append(N)
assert lu.product(factors) == norig, (str(factors) + (", %d != %d" % (lu.product(factors), norig)))
return factors
def numDivisors(N): factors = factorTrialDivision(N) return lu.product(lu.addOne(lu.listCount(factors)))
if prod > maxprod: maxprod = prod print maxprod ##################################################################### # Problem 12 if problem == 12: val = 0 for x in xrange(9,50000): # Find prime factors of n*(n-1)/2 numdiv = 0 if x % 2 == 0: factorx = pf.factorTrialDivision(x//2) factorx1 = pf.factorTrialDivision(x+1) factorx.extend(factorx1) numdiv = lu.product(lu.addOne(lu.listCount(factorx))) else: factorx = pf.factorTrialDivision(x) factorx1 = pf.factorTrialDivision((x+1)//2) factorx.extend(factorx1) numdiv = lu.product(lu.addOne(lu.listCount(factorx))) if (numdiv) >= 500: val = x break print nf.cumsum(val) ##################################################################### # Problem 13 # OK I cheated... thank you big number library of python if problem == 13:
