import math
from functools import reduce
import time

def primeFactors(n):
    i = 2
    factors = {}
    num = 0
    while i ** 2 <= n:
            if n % i:
                i += 1
            else:
                n //= i
            num = factors.get(i, None)
            if num is None:
                factors[i] = 1
            else:
                factors[i] = num+1 
    if n > 1:
        num = factors.get(n, None)
        if num is None:
            factors[n] = 1
        else:
            factors[n] = num+1
    return factors

start_time = time.time()
numOfDivisors = 500
n = 2

while True:
    t = int(n*(n+1)/2)
    factors = primeFactors(t).values()

    if reduce(lambda x, y: x*y, [t+1 for t in factors]) >= numOfDivisors:
        print(t)
        break
    else:
        n += 1

print("----%s seconds ----" % (time.time() - start_time))

import math
import time

def primeFactors(n):
    i = 2
    factors = {}
    num = 0
    while i ** 2 <= n:
            if n % i:
                i += 1
            else:
                n //= i
            num = factors.get(i, None)
            if num is None:
                factors[i] = 1
            else:
                factors[i] = num+1 
    if n > 1:
        num = factors.get(n, None)
        if num is None:
            factors[n] = 1
        else:
            factors[n] = num+1
    return factors

start_time = time.time()
numOfDivisors = 500
n = 2

while True:
    t = int(n*(n+1)/2)
    factors = primeFactors(t).values()

    k = 1
    for i in factors:
        k *= (i+1)

    if k >= numOfDivisors:
        print(t)
        break
    else:
        n += 1

print("----%s seconds ----" % (time.time() - start_time))

import math
from functools import reduce
import time

def primeFactors(n):
    i = 2
    factors = {}
    num = 0
    while i ** 2 <= n:
        if n % i:
            i += 1
        else:
            n //= i
            num = factors.get(i, None)
            if num is None:
                factors[i] = 1
            else:
                factors[i] = num+1 
    if n > 1:
        num = factors.get(n, None)
        if num is None:
            factors[n] = 1
        else:
            factors[n] = num+1
    return factors

start_time = time.time()
numOfDivisors = 500
n = 2

while True:
    t = int(n*(n+1)/2)
    factors = primeFactors(t).values()

    if reduce(lambda x, y: x*y, [t+1 for t in factors]) >= numOfDivisors:
        print(t)
        break
    else:
        n += 1

print("----%s seconds ----" % (time.time() - start_time))

import math
import time

def primeFactors(n):
    i = 2
    factors = {}
    num = 0
    while i ** 2 <= n:
        if n % i:
            i += 1
        else:
            n //= i
            num = factors.get(i, None)
            if num is None:
                factors[i] = 1
            else:
                factors[i] = num+1 
    if n > 1:
        num = factors.get(n, None)
        if num is None:
            factors[n] = 1
        else:
            factors[n] = num+1
    return factors

start_time = time.time()
numOfDivisors = 500
n = 2

while True:
    t = int(n*(n+1)/2)
    factors = primeFactors(t).values()

    k = 1
    for i in factors:
        k *= (i+1)

    if k >= numOfDivisors:
        print(t)
        break
    else:
        n += 1

print("----%s seconds ----" % (time.time() - start_time))

I'm trying to solve problem 12 on Project Euler website, which reads as:

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?

I have solved problem 12 on Project Euler website, which reads:

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?