2019 AIME I Problem 9

Let \tau(n) denote the number of positive integer divisors of n. Find the sum of the six least positive integers n that are solutions to \tau (n) + \tau (n+1) = 7.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.