# Find the sum of the prime factors of choose(20000000, 15000000)
from useful import PrimeList, primeFactorize
n = 20000000
r = 15000000
primes = PrimeList(n + 2)
toplist = range(15000001,20000001))
bottomlist = range(2,15000001)
topdict = {}
bottomdict = {}
for num in toplist :
topdict[num] = 1
for num in bottomdict :
bottomdict[num] = 1
for (num, count) in topdict.items() :
total += sum(primeFactorize(num))
for num in bottomlist :
print num
total -= sum(primeFactorize(num))
print total
# Find all numbers x that can be factored into x=ab such that x, a, and b contain each digit 1 through 9 exactly once. # Let us generate all 4 or 5-digit numbers that are composed of unique digits. from useful import primeFactorize, digits sum = 0 for i in range (1000, 10000) : dList = digits(i) if (len(set(dList)) != len(dList) or 0 in dList) : continue factors = primeFactorize(i) for j in range(2**len(factors)) : num1 = 1 num2 = 1 for k in range(len(factors)) : if j/(k+1) == 1 : num1 *= factors[k] else : num2 *= factors[k] allDigits = dList + digits(num1) + digits(num2) if (len(allDigits) == 9 and len(set(allDigits)) == 9 and 0 not in allDigits) : print i, num1, num2, "!" sum += i break print sum
from useful import primeFactorize
dict = {}
for x in xrange(2,100001) :
facts = primeFactorize(x)
rad = frozenset(facts)
if rad in dict :
dict[rad].append(x)
else :
dict[rad] = [x]
tosort = []
for key in dict.keys() :
prod = 1
for fact in key :
prod *= fact
tosort.append((prod, key))
tosort.sort()
lower = 0
target = 10000
for (prod, rad) in tosort :
if (lower + len(dict[rad]) < target) :
lower += len(dict[rad])
continue
lis = dict[rad]
lis.sort()
