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solution_3.py
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59 lines (45 loc) · 1.2 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 functools import reduce
from itertools import count
def trianglenums():
for n in count(start=1, step=1):
yield n * (n + 1) // 2
def divisors(n):
exps = []
i = 2
while n > 1:
count = 0
while n % i == 0:
n /= i
count += 1
if count != 0:
exps.append(count + 1)
i += 1
return reduce(lambda x, y: x * y, exps, 1)
for i in trianglenums():
if divisors(i) > 500:
print(i)
quit()