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?

- Code: Select all
`: nbDivisors(n) // ( n -- n ) : Returns number of divisors of n`

{

| sqrtn i |

0 n sqrt asInteger dup ->sqrtn loop: i [ n i mod ifFalse: [ 2 + ] ]

n sqrtn sq == -

}

: pe012(n) // ( n -- ) : Calculate first triangle number to have over n divisors

{

| tr |

1 ->tr

1 while ( tr nbDivisors n < ) [ 1 + dup tr + ->tr ] drop tr

}