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solution_1.py
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75 lines (56 loc) · 1.68 KB
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#!/usr/bin/env python
# coding=utf-8
# Python Script
#
# Copyleft © Manoel Vilela
#
#
# Highly divisible triangular number
# Problem 12
# The sequence of triangle numbers is generated by adding the natural numbers.
# So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.
# The first ten terms would be:
# 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
# Let us list the factors of the first seven triangle numbers:
# 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 itertools import combinations, count
from functools import reduce
def trianglenums():
for n in count(start=1, step=1):
yield n * (n + 1) // 2
def factoring(n):
divs = [1]
i = 2
while n > 1:
while not n % i:
n /= i
divs.append(i)
i += 1
return divs
def divisors(n):
divs = factoring(n)
primes = divs[1:]
for j in range(1, len(primes)):
for comb in combinations(primes, j + 1):
newdiv = reduce(lambda x, y: x*y, comb)
if newdiv <= n and newdiv not in divs:
divs.append(newdiv)
return len(divs)
# external thing whose I found on thread of that problem
# resuming all (one line! D:) FDP! (divisors + factoring function).
# The perfomance it's the same
def factors(n):
return set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n ** 0.5) + 1) if not n % i)))
for i in trianglenums():
if divisors(i) > 500:
print(i)
break