mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
46 lines
935 B
Python
46 lines
935 B
Python
from __future__ import print_function
|
|
from math import sqrt
|
|
'''
|
|
Highly divisible triangular numbers
|
|
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?
|
|
'''
|
|
try:
|
|
xrange #Python 2
|
|
except NameError:
|
|
xrange = range #Python 3
|
|
|
|
def count_divisors(n):
|
|
nDivisors = 0
|
|
for i in xrange(1, int(sqrt(n))+1):
|
|
if n%i == 0:
|
|
nDivisors += 2
|
|
|
|
return nDivisors
|
|
|
|
tNum = 1
|
|
i = 1
|
|
|
|
while True:
|
|
i += 1
|
|
tNum += i
|
|
|
|
if count_divisors(tNum) > 500:
|
|
break
|
|
|
|
print(tNum) |