12.q

args:.Q.def[`name`port!("euler12";8888);].Q.opt .z.x

/ remove this line when using in production
/ euler12:localhost:8888::
{ if[not x=0; @[x;"\\\\";()]]; value"\\p 8888"; } @[hopen;`:localhost:8888;0];


/
The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. 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.

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

tri:sum 1+ til @

fac:{s where f = floor f:x % s:1+til x}

(count fac tri@) each 1+ til 7