# An Infinite Sequence of Positive Integers!

**Number Theory**Level 5

Suppose there is an infinite sequence of positive integers such that the first term is 16, the number of distinct positive divisors of each term is divisible by 5, and the terms of the sequence form an arithmetic progression. Of all such sequences, find the one with the smallest possible non-zero common difference between consecutive terms. Submit that smallest common difference you obtained as your answer.