Problem #222
Houdini and Picking Cards
Houdini has a deck consisting of 10^6 cards, where the i-th card (starting with 1) is labeled with the number i. He randomly picks two cards from the deck, and wants to find the probability that one of the card labels is divisible by the other. The probability can be written in the form \frac{m}{n} where m and n are coprime integers. Enter your answer as m + n.