First triangle number with 500 divisors

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August undefined, 2024

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 WebSep 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: …

My C++ solution for Project Euler 12: Highly divisible triangular number

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: (triangle_number_search 500I);; -> 76576500I So, the first triangle number to have over 500 divisors is: 76576500 (btw, it has 576 divisors) (and as you can see, I’m still not … WebJul 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 … cst 410 icms

Find the first Triangular number which has 50 factors?

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: … WebThe task is to find a triangle number which has at least 500 divisors. For example 28 has 6 divisors: 1,2,4,7,14,28 My code works for up to 200 divisors, but for 500 it runs … 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 … cst412mf toto

Python: Find the first triangle number to have over n …

Project Euler: #12 - Highly divisible triangular number

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. 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 … cst 4129tWebWe 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? The first thing I did was to generate 2 functions, one for determining the nth triangular number, and the other for determining number of factors. Both these were fairly simple functions: cst416m toto

"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: " - First triangle number with 500 divisors

First triangle number with 500 divisors

First triangle number to have over five hundred divisors - Scatt…

WebJul 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, … WebAll Algorithms implemented in Python. Contribute to saitejamanchi/TheAlgorithms-Python development by creating an account on GitHub.

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WebHackerRank Project Euler 12 wants us to find the first triangle number to have over 1 ≤ N ≤ 1000 divisors; extending the number of divisors from 500 and running 10 test cases. This algorithm calculates the answer for 1000 in 70ms. Python Source Code view raw Project-Euler-Problem-12.py hosted with by GitHub 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.

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 WebAug 16, 2012 · #include using namespace std; int triangle_numbers (int n, int meh = 0) { int count = 0; //calculate how many divisors there are for meh for (int i = 1; i 500) return …

WebFeb 16, 2024 · The six divisors of 28 are 1, 2, 4, 7, 14 and 28. The code to solve Project Euler 12 is shown below. The loop continues until it finds a triangular number with 500 … 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 …

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.

cst446cemfg1WebMar 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. cst446cemfg01WebThe 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 … cst 4257tWebOct 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... early childhood 意味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 … early child intervention njWebDec 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. early child marriages in zimbabweWebOct 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 … cst454cefg#11