What is the value of the first triangle number to have over divisors?

What is the value of the first triangle number to have over divisors?

We can see that 28 is the first triangle number to have over five divisors.

How do you find n in a triangular number?

Triangular numbers are a pattern of numbers that form equilateral triangles. The formula for calculating the nth triangular number is: T = (n)(n + 1) / 2.

How do you find all triangular numbers?

Triangular Number Sequence

1. The first triangle has just one dot.
2. The second triangle has another row with 2 extra dots, making 1 + 2 = 3.
3. The third triangle has another row with 3 extra dots, making 1 + 2 + 3 = 6.
4. The fourth has 1 + 2 + 3 + 4 = 10.
5. etc!

How do you find a number with N divisors?

2 Answers

1. Some observations: If p is a prime, then pn−1 has exactly n divisors.
2. And that’s the only way we can find numbers with exactly n divisors: We write n as a product n = n1 * n2 * n3 …, then find primes p1, p2, p3 and so on, and the product p1n1−1p2n2−1p3n3−1… has exactly n divisors.

Which is the first triangular number?

Maths in a minute: Triangular numbers A triangular number is a number that can be represented by a pattern of dots arranged in an equilateral triangle with the same number of dots on each side. The first triangular number is 1, the second is 3, the third is 6, the fourth 10, the fifth 15, and so on.

Which of the following is a triangular number?

List Of Triangular Numbers. 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120,136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, and so on.

How to find a highly divisible triangular number?

Second Step: Starting at the number found in the previous step, search for the next triangle number. Check to see whether this number has 500+ divisors. If yes, this is the number we were looking for, else…

Which is the first triangular number of N?

Given a number N, find the first triangular number whose number of divisors exceeds N. Triangular numbers are sums of natural numbers, i. e., of the form x* (x+1)/2. First few triangular numbers are 1, 3, 6, 10, 15, 21, 28, …

What’s the fourth step of the triangle equation?

Fourth Step: Add (n+1) to the last triangle number found, to find the next triangle number. Check whether this number has 500+ divisors. If yes, this number is the answer. If not, repeat Fourth Step till the process terminates. The First Step isn’t exactly a piece of cake, but necessary to reduce computation time.

What to do when the number of divisors exceeds n?

A naive solution is to iterate for every triangular number and count the number of divisors using the Sieve method. At any moment if the number of divisors exceeds the given number N, then we get our answer.