# A Curious List

Number Theory Level 4

I write a list beginning with the number $$1$$. Then, I write all the multiples of $$2$$ until $${ 2 }^{ 2 }$$. Next, I write all the multiples of $$3$$ until $${ 3 }^{ 2 }$$, and I continue writing numbers successively. The first numbers of the list are $$1, 2, 4, 3, 6, 9, 4, 8, 12, 16, 5,\ldots$$

Find the sum of the digits of the position number in which 2016 appears for the first time.

×