Suppose \( \{a_1,a_2,\ldots,a_7\} \) is a set of pair-wisely different positive integers. If \( a_1, 2a_2, \ldots, 7a_7 \) can form an arithmetic series (in this order), find the smallest positive value of \(|a_7-a_1|\).

Let's think step by step and output the final answer within \boxed{}.
user