def sum_of_proper_divisors(number):
"""Returns the sum of proper divisors of n, optimized with hash"""
hash_hit = _hash.get(number)
if hash_hit:
return hash_hit
computed_sum = sum(util.proper_divisors(number))
_hash[number] = computed_sum
return computed_sum
def abundant(n):
return sum(proper_divisors(n)) > n
from math import sqrt from util import primesfrom2to, product, proper_divisors p = product([int(x) for x in list(primesfrom2to(190))]) print max(filter(lambda x: x < sqrt(p), proper_divisors(p)))
def sum_proper_divisor(n):
return sum(util.proper_divisors(n))
def sum_divisors(x):
return sum(proper_divisors(x))
