Project Euler

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^th 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?

Iterators again.

import math
 
def divisors(n):
  """
  Find all divisors of n by trial division
  """
  divisors = set([1])
  for i in range(1, math.ceil(n ** 0.5)+1):
      if n % i == 0:
        divisors.add(i)
        divisors.add(n/i)
  return divisors
 
class Triangle:
  def __init__(self):
    self.count = 1
    self.sum = 0
  def __iter__(self):
    return self
  def next(self):
    self.sum += self.count
    self.count += 1
    return self.sum
 
def problem12(n):
  t = Triangle()
  while True:
    x = t.next()
    num = len(divisors(x))
    if num > n:
      return x, num
 
>>> problem12(500)
problem12 took 6172.000 ms
(76576500, 576)

Tags: divisors, factors, iterator, problem12, project euler, python, triangle number

This entry was posted on Tuesday, February 10th, 2009 at 9:37 am and is filed under factors. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.