def answer(num):
""" returns the sum of all primes below num """
triangle_gen = triangle_numbers()
n_factors = 1
while n_factors <= num:
guess = next(triangle_gen)
n_factors = num_factors(guess)
return guess
def answer(num):
""" returns the sum of all primes below num """
triangle_gen = triangle_numbers()
n_factors = 1
while n_factors <= num:
guess = next(triangle_gen)
n_factors = num_factors(guess)
return guess
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?
Approach:
** Divisors method **
Use the prime.py from s-anand
"""
import prime
for i in range(1, 1000000000):
n = i * (i+1) / 2
if prime.num_factors(n) > 500:
print(n)
break
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?
Approach:
** Divisors method **
Use the prime.py from s-anand
"""
import prime
for i in range(1, 1000000000):
n = i * (i + 1) / 2
if prime.num_factors(n) > 500:
print(n)
break
import prime
i = 1
tri = sum(xrange(i))
while prime.num_factors(tri) < 500:
tri, i = tri+i, i+1
print tri
