euler-012

require 'prime'

triangle_number_index = 1
loop do
  # Calculate the nth triangle number
  triangle_number = (triangle_number_index * (triangle_number_index + 1)) / 2

  # Get the prime factorization of the triangle number
  prime_factors = triangle_number.prime_division

  # Calculate the number of divisors
  # For each prime factor p^a, it contributes (a+1) to the divisor count
  # The total divisor count is the product of these contributions
  divisor_count = prime_factors.map { |base, power| power + 1 }.reduce(:*)
  
  if divisor_count > 500
    puts "First triangle number with over 500 divisors: #{triangle_number}"
    puts "This is triangle number ##{triangle_number_index}"
    break
  end
  
  triangle_number_index += 1
end