WebJul 7, 2012 · Use the first equation to calculate the first triangle number, and check whether the sum of divisors more than 500; if not (definitely not, the first is 1), move on to the next triangle number till you find the result. However, this is so slow that I could’t take it. Using so-called integer factorization would speed up a lot. WebAug 19, 2024 · A triangular number is calculated by the equation: n (n+1)/2 The factors of the first five triangle numbers: 1: 1 3: 1, 3 6: 1, 2, 3, 6 10: 1, 2, 5, 10 15: 1, 3, 5, 15 In the above list 6 is the first triangle number to …
Did you know?
WebDec 27, 2014 · The solution to the problem "the first number that has 500 divisors" results in a number somewhat larger than 75,000,000. That is somewhat after the 12-thousandth triangle number. So, in this case, you are looping through 12,000 times, and that's the same regardless of whether you use your old, or your new getDivisorCount method. WebWe'll still have to make sure the number is triangular at the end. # 500 = 2^2 * 5^3, so the ki's are either 1 or 4, and there are 2 1's, and 3 4's # or the ki could be 24 or 124 as well but I think those will generate numbers …
WebConsider the sum S = ∑ k = 1 n k As I was computing the first triangle number with over 500 divisors (Project Euler), I came across the hypothesis that most triangle numbers have an even number of divisors (if n = 8, then S = 36 has 9 divisors). Example: WebJan 28, 2009 · Values let mutable divisor_count = 1I for exponent in exponents do divisor_count. This took less than a minute to run and running it gives: …
Webtriangle = 1 for natural in range (2,1000000): triangle += natural if divisors (triangle) >= 500: print triangle break The following is useless and should be removed to reduce clutter (it also speeds the programme up a tiny bit else: continue WebDec 25, 2014 · What is the value of the first triangle number to have over five hundred divisors? The N 'th triangle number is the sum of all natural numbers from 1 to N, for …
WebThis will create a set and put all of factors of number n into it. Second, use while loop until you get 500 factors: a = 1 x = 1 while len(factors(a)) < 501: x += 1 a += x This loop will …
WebApr 14, 2016 · 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. fisherman creations crab pot treeWebMar 30, 2024 · What is the value of the first triangle number to have over five hundred divisors? My Algorithm Similar to other problems, my solution consists of two steps 1. precompute all possible inputs 2. for each test case: perform a simple lookup It takes less than a second to find all such numbers with at most 1000 divisors. fisherman creekWebOct 5, 2024 · The programm first calls the divisor-function, then calculates the triangle number for n, then checks whether the number is prime or not, and if it is, it directly … fisherman cove flatbush junctionWebJul 9, 2013 · Triangle number #12375 = 76576500 is the first one that has at least 500 factors (actually 576 factors): 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, ..., 19144125, 25525500, … canadian technology after ww2WebJan 12, 2024 · We need to find the first triangular number that has over 500 divisors. Approach This is an interesting problem involving triangular numbers. More on triangular numbers on this wiki page. If we are to find the nth triangular number, then we can use the formula, T n = n ( n + 1) 2 fisherman cove flint miWebSep 1, 2015 · Problem 12 of Project Euler asks for the first triangle number with more than 500 divisors. These are the factors of the first seven triangle numbers: ∑1 = 1: 1 ∑2 = 3: 1,3 ∑3 = 6: 1,2,3,6 ∑4 = 10: 1,2,5,10 ∑5 = 15: 1,3,5,15 ∑6 = 21: 1,3,7,21 ∑7 = 28: 1,2,4,7,14,28 Here’s how I proceeded: First Step: Find the smallest number with 500 … fisherman craftWebWe 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? Solution The number of divisors of a natural number n n is given by tau (n) or \tau (n) τ (n) or sometimes \delta (n) δ(n) as mentioned here already. canadian technical tape ltd