Euler project 12: triangle number

I am writing this only because I find these simple math trick is like magic.
Triangle number is ones composed by adding previous number together, like the additive analog of factorial number: Tn = 1 + 2 + 3 + ... + n. Now it asks what is the first triangle number with more than 500 divisors?

There are several ways to generate a triangle number. One is use the plain equation to sum up; other one is clearly use the sum-up equation Tn = n*(n-1)/2. However, since what we basically need here is to iterate all triangle numbers starts with 1 (or some bigger yet still small number), I add a step every time using Tn = Tn-1 + n. I think latter two should be mostly at the same speed.

Another thing is to find the number of divisors for a number. This is just iterate from 1 to sqrt(n), according to many math properties. Also since divisors appear in pairs, one might add two every time it finds a fit one if one uses this method; but minus one if the divisor it finds happens to be the sqrt(n).

Codes:

	from math import sqrt, floor
	def euler12():
	D = 0
	n = 1
	step = 2
	while D < 500:
	n += step
	step += 1
	D = findDivisor(n)
	return n
	def findDivisor(m):
	d = 2
	for i in range(2,int(floor(sqrt(m)))):
	if m%i == 0:
	d += 2
	if m/i == i:
	d -= 1
	return d
	if __name__ == '__main__':
	print euler12()

view raw gistfile1.py hosted with ❤ by GitHub