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: 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 …
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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. WebThe following is a solution to Project Euler problem number 12: which is to find the first triangular number with more than 500 divisors. The code takes far too long to complete …
WebSep 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 … WebOct 11, 2011 · In one of the problems that I'm solving on Project Euler, I'm trying to find the first triangle number that has 500 divisors. However, the thing is that my code slows to a crawl after three million. I only have two variables, no macros, no global variables, I'm not storing a triangle number but...
WebWe 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. 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.
WebJan 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
WebFeb 15, 2024 · The loop continues until it finds a triangular number with 500 divisors. The first two lines increment the index and create the next triangular number. The third line in the loop determines the number of times each factor is repeated (the run lengths). The last line calculates the number of divisors using the above-mentioned formula. town clerk plymouth nhWebAug 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 … power eagle pressure washersWebJul 29, 2024 · First few triangular numbers are 1, 3, 6, 10, 15, 21, 28, … Examples: Input: N = 2 Output: 6 6 is the first triangular number with more than 2 factors. Input: N = 4 … power eagle 1000WebWe'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 … powereadingWebSep 10, 2024 · 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: … powerdyne supercharger pulleysWebThis 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 … town clerk plymouth maWebMar 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. powerdyne supercharger instructions