def distinct_prime_factor_count(n):
f = factors(n) - set([1, n])
prime_factors = set([])
for p in f:
if isprime(p):
prime_factors.add(p)
return len(prime_factors)
def main(limit: int):
"""Return the triangle number with factors over the limit.
:return: Triangle number with over the `limit` divisors.
"""
for triangle_number in triangle_number_generator():
if len(factors(triangle_number)) > limit:
return triangle_number
else:
continue
def is_abundant(n):
fs = factors(n)
fs.remove(n)
s = 0
for f in fs:
s += f
if s > n:
return True
else:
return False
#!/usr/bin/python from common import factors #set the total to 0 total = 0 #go through all numbers (1, 10000] for a in range(1, 10000): b = sum(factors(a)) #if d(a) == d(b) and a != b add to total if a != b and a == sum(factors(b)): total += a #print the total print total
from common import factors
N = 999 * 999
def palindrome(num):
num = str(num)
n = len(num) // 2
if num[0:n][::-1] == num[n if n % 2 != 0 else n + 1 : ]:
return True
else:
return False
#Check to see if there is a factor of length 3 that matches with another length 3 factor.
def check_factors(factors, n) :
factors = filter(lambda x: len(str(x)) == 3, factors)
for i in factors:
if(len(str(n/i)) == 3):
print i, n/i
return True
for i in xrange(N, 100 * 100, -1):
if palindrome(i) and check_factors(factors(i), i):
print 'Biggest Palindrome is ', i
break;
if i > value/2: return False tmp = abundantNumbers.index(value-i) return True except: continue return False #largest number that can't be written as sum of 2 abundeant numbers maxNumber = 28123 #list of abundunt numbers abundantNumbers = [] #sum of numbers that cant be added up by 2 abundant numbers total = 0 #go through all numbers below max for i in range(1, maxNumber+1): #get the sum of the factors and append to abundant if it is if sum(factors(i)) > i: abundantNumbers.append(i) #if it is now abundant add to total if not isAbundant(i): total += i print total
# Problem 3 # 02 November 2001 # The prime factors of 13195 are 5, 7, 13 and 29. # What is the largest prime factor of the number 600851475143 ? from common import factors print(list(factors(600851475143))[-1])
#!/usr/bin/env python
from common import factors
def triangle_number(n):
return sum(xrange(n+1))
for n in xrange(2, 100000):
tn = triangle_number(n)
ln = len(factors(tn))
#print n, tn, ln
if ln > 100:
print "Over 100 factors ", n, tn, ln
if ln > 500:
print "Over 500 factors ", n, tn, ln
break
def prime_factors(n, sieve):
f = factors(n)
f.remove(1)
f.remove(n)
return [i for i in f if sieve[i]]
