def largestprimefactor(n):
if type(n) is not int and type(n) is not long:
raise TypeError
allfactors = factors(n)
# Now we have a list of factor pairs (non-prime)
# Let's find which of these are prime numbers
pfactors = []
for factorpair in allfactors:
if isprime(factorpair[0]):
pfactors.append(factorpair[0])
if isprime(factorpair[1]):
pfactors.append(factorpair[1])
# print(pfactors)
return max(pfactors)
def d(n):
# Sum of proper divisors of n
s = 0
pairs = factors(n)
for pair in pairs:
if pair[0] == pair[1]:
# count divisors only once
s += pair[0]
elif pair[0] == 1:
# Don't add n
s += pair[0]
else:
s += pair[0]
s += pair[1]
return s
def primeFactors(n, conv=False):
prime_factors = {}
for pair in factors(n):
for num in pair:
if isprime(num):
prime_factors[num] = 1
prod = 1
for prime_factor in prime_factors:
prod = prod * prime_factor
while prod != n:
quotient = n / prod # i.e. what we still need to represent with the prime factors
for prime_factor in prime_factors:
if quotient % prime_factor == 0:
prod = prod * prime_factor
prime_factors[prime_factor] += 1
if conv is False:
return prime_factors
else:
return primefactorconverter(prime_factors)
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred divisors?
"""
from lib import factors
triangle=1
last=2
f=factors()
while True:
triangle=triangle+last
last=last+1
k=f.factor_count(triangle)
if k>500:
break
print(triangle)
def method_max(N):
return max(factors(N))
def len_fac(n):
return len(set(lib.factors(n)))
def method_max(N): return max(factors(N))
def smallest_divisible(min_, max_): facts = mset() for i in range(min_, max_+1): facts += mset(factors(i)) - facts return reduce(mul, facts.elements(), 1)