Project Eueler: problem12

問題

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?

回答

require "mathn"
tnum = 1
(2..100000).each do |n|
  #calc triangle number
  tnum += n
  #calc prime division
  pdiv = tnum.prime_division
  #calc divisors
  divs = pdiv.inject(1){|sum,i| sum * (i[1]+1)}
  if divs >= 500
    p n, tnum, pdiv, divs
    break
  end
end

数分かかる。重い。