=begin

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 the 7th triangle number, 28, is the first triangle number to have over five divisors.

Which is the first triangle number to have over five-hundred divisors?

=end


ordinal = 0
triangle = 0
while true
  factornum = 0
  ordinal += 1
  triangle += ordinal
  print(triangle.to_s+"\n")
  Math.sqrt(triangle).floor.downto 1 do |n|
    qt = triangle / n.to_f
    if qt == n
      factornum += 1
    elsif qt == qt.truncate
      factornum += 2
    end
  end
  if factornum > 500
    print(triangle.to_s+' has '+factornum.to_s+' factors.')
    break
  end
end