def d(n):
return sum(
naturalFactors(n)[:-1]
) # return sum of all "proper divisors" of n, "proper divisors of n" = naturalFactors except n itself
Problem 12 - Highly divisible triangular number
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 modules.matlib import nthTriangle, naturalFactors
i = nthTriangle(500) # start with i of 500-th triangle number
trg = nthTriangle(i) # triangle is
while len(naturalFactors(trg)) <= 500: # while number of natural factors isn't over 500
i += 1 # next index
trg = nthTriangle(i) # triangle is
print(trg) # output first triangle with more than 500 natural divisors