Problem 179 Published on Saturday, 26th January 2008, 05:00 am; Solved by 9690; Difficulty rating: 25%

Find the number of integers 1 < n < 10^{7}, for which n and n + 1 have the same number of positive divisors. For example, 14 has the positive divisors 1, 2, 7, 14 while 15 has 1, 3, 5, 15.